361924
A ball is projected horizontally from the top of the tower with a velocity \({v_0}\). It will be moving at angle of \(60^\circ \) with the horizontal afte time.
361925
A ball rolls off the top of a staircase with a horizontal velocity \(u\) \(m\)/\(s\). If the steps are \(h\) metre high and \(b\) metre wide, the ball will hit the edge of the \(n\)th step, if:
1 \(n = \frac{{2hu}}{{g{b^2}}}\)
2 \(n = \frac{{2h{u^2}}}{{gb}}\)
3 \(n = \frac{{2h{u^2}}}{{g{b^2}}}\)
4 \(n = \frac{{h{u^2}}}{{g{b^2}}}\)
Explanation:
If the ball hits the nth step, then horizontal distance traversed \( = nh\) Here, velocity along horizontal direction \( = u\) Velocity along vertical direction \( = 0\) \(\therefore \;\;nb = ut\) \(nh = 0 + \frac{1}{2}g{t^2}\) From (1) \(t = \frac{{nb}}{v},\;\therefore nh = \frac{1}{2}g \times {\left( {\frac{{nb}}{u}} \right)^2}\) \(n = \frac{{2h{u^2}}}{{g{b^2}}}\)
PHXI04:MOTION IN A PLANE
361926
A body is projected horizontally with velocity \(196\;m{s^{ - 1}}\) from height \(400\;m.\) What is the time to reach the ground?
361927
A staircase contains three steps each 10 \(cm\) high and 20 \(cm\) wide. What should be the minimum horizontal velocity of the ball rolling off the uppermost plane so as to hit directly the lowest plane?
1 \(7\,m{s^{ - 1}}\)
2 \(2\,m{s^{ - 1}}\)
3 \(4\,m{s^{ - 1}}\)
4 \(10\,m{s^{ - 1}}\)
Explanation:
At minimum velocity, it will move just touching point \(E\) reaching the ground. \(A\) is the origin of reference co-ordinate. If \(u\) is the minimum speed \(\begin{aligned}& x=40, y=20, \theta=0^{\circ} \\& y=\tan \theta-g \dfrac{x^{2} \sec ^{2} \theta}{2 u^{2}}\end{aligned}\) where \(g=10 {~ms}^{-2}\) \(=1000 {~cm} {~s}^{-2}\) \(\begin{aligned}& -20=-\dfrac{800000}{2 u^{2}} \\& u=200 {~cm} {~s}^{-1}=2 {~ms}^{-1}\end{aligned}\)
PHXI04:MOTION IN A PLANE
361928
If a body is projected with an angle \(\theta \) to the horizontal, then
1 Its velocity is always prependicular to its acceleration
2 Its velocity becomes zero at its maximum height
3 Its velocity makes zero angle with the horizontal at its maximum height
4 The body just before hitting the ground, the direction of velocity coincides with the accleration
361924
A ball is projected horizontally from the top of the tower with a velocity \({v_0}\). It will be moving at angle of \(60^\circ \) with the horizontal afte time.
361925
A ball rolls off the top of a staircase with a horizontal velocity \(u\) \(m\)/\(s\). If the steps are \(h\) metre high and \(b\) metre wide, the ball will hit the edge of the \(n\)th step, if:
1 \(n = \frac{{2hu}}{{g{b^2}}}\)
2 \(n = \frac{{2h{u^2}}}{{gb}}\)
3 \(n = \frac{{2h{u^2}}}{{g{b^2}}}\)
4 \(n = \frac{{h{u^2}}}{{g{b^2}}}\)
Explanation:
If the ball hits the nth step, then horizontal distance traversed \( = nh\) Here, velocity along horizontal direction \( = u\) Velocity along vertical direction \( = 0\) \(\therefore \;\;nb = ut\) \(nh = 0 + \frac{1}{2}g{t^2}\) From (1) \(t = \frac{{nb}}{v},\;\therefore nh = \frac{1}{2}g \times {\left( {\frac{{nb}}{u}} \right)^2}\) \(n = \frac{{2h{u^2}}}{{g{b^2}}}\)
PHXI04:MOTION IN A PLANE
361926
A body is projected horizontally with velocity \(196\;m{s^{ - 1}}\) from height \(400\;m.\) What is the time to reach the ground?
361927
A staircase contains three steps each 10 \(cm\) high and 20 \(cm\) wide. What should be the minimum horizontal velocity of the ball rolling off the uppermost plane so as to hit directly the lowest plane?
1 \(7\,m{s^{ - 1}}\)
2 \(2\,m{s^{ - 1}}\)
3 \(4\,m{s^{ - 1}}\)
4 \(10\,m{s^{ - 1}}\)
Explanation:
At minimum velocity, it will move just touching point \(E\) reaching the ground. \(A\) is the origin of reference co-ordinate. If \(u\) is the minimum speed \(\begin{aligned}& x=40, y=20, \theta=0^{\circ} \\& y=\tan \theta-g \dfrac{x^{2} \sec ^{2} \theta}{2 u^{2}}\end{aligned}\) where \(g=10 {~ms}^{-2}\) \(=1000 {~cm} {~s}^{-2}\) \(\begin{aligned}& -20=-\dfrac{800000}{2 u^{2}} \\& u=200 {~cm} {~s}^{-1}=2 {~ms}^{-1}\end{aligned}\)
PHXI04:MOTION IN A PLANE
361928
If a body is projected with an angle \(\theta \) to the horizontal, then
1 Its velocity is always prependicular to its acceleration
2 Its velocity becomes zero at its maximum height
3 Its velocity makes zero angle with the horizontal at its maximum height
4 The body just before hitting the ground, the direction of velocity coincides with the accleration
361924
A ball is projected horizontally from the top of the tower with a velocity \({v_0}\). It will be moving at angle of \(60^\circ \) with the horizontal afte time.
361925
A ball rolls off the top of a staircase with a horizontal velocity \(u\) \(m\)/\(s\). If the steps are \(h\) metre high and \(b\) metre wide, the ball will hit the edge of the \(n\)th step, if:
1 \(n = \frac{{2hu}}{{g{b^2}}}\)
2 \(n = \frac{{2h{u^2}}}{{gb}}\)
3 \(n = \frac{{2h{u^2}}}{{g{b^2}}}\)
4 \(n = \frac{{h{u^2}}}{{g{b^2}}}\)
Explanation:
If the ball hits the nth step, then horizontal distance traversed \( = nh\) Here, velocity along horizontal direction \( = u\) Velocity along vertical direction \( = 0\) \(\therefore \;\;nb = ut\) \(nh = 0 + \frac{1}{2}g{t^2}\) From (1) \(t = \frac{{nb}}{v},\;\therefore nh = \frac{1}{2}g \times {\left( {\frac{{nb}}{u}} \right)^2}\) \(n = \frac{{2h{u^2}}}{{g{b^2}}}\)
PHXI04:MOTION IN A PLANE
361926
A body is projected horizontally with velocity \(196\;m{s^{ - 1}}\) from height \(400\;m.\) What is the time to reach the ground?
361927
A staircase contains three steps each 10 \(cm\) high and 20 \(cm\) wide. What should be the minimum horizontal velocity of the ball rolling off the uppermost plane so as to hit directly the lowest plane?
1 \(7\,m{s^{ - 1}}\)
2 \(2\,m{s^{ - 1}}\)
3 \(4\,m{s^{ - 1}}\)
4 \(10\,m{s^{ - 1}}\)
Explanation:
At minimum velocity, it will move just touching point \(E\) reaching the ground. \(A\) is the origin of reference co-ordinate. If \(u\) is the minimum speed \(\begin{aligned}& x=40, y=20, \theta=0^{\circ} \\& y=\tan \theta-g \dfrac{x^{2} \sec ^{2} \theta}{2 u^{2}}\end{aligned}\) where \(g=10 {~ms}^{-2}\) \(=1000 {~cm} {~s}^{-2}\) \(\begin{aligned}& -20=-\dfrac{800000}{2 u^{2}} \\& u=200 {~cm} {~s}^{-1}=2 {~ms}^{-1}\end{aligned}\)
PHXI04:MOTION IN A PLANE
361928
If a body is projected with an angle \(\theta \) to the horizontal, then
1 Its velocity is always prependicular to its acceleration
2 Its velocity becomes zero at its maximum height
3 Its velocity makes zero angle with the horizontal at its maximum height
4 The body just before hitting the ground, the direction of velocity coincides with the accleration
NEET Test Series from KOTA - 10 Papers In MS WORD
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PHXI04:MOTION IN A PLANE
361924
A ball is projected horizontally from the top of the tower with a velocity \({v_0}\). It will be moving at angle of \(60^\circ \) with the horizontal afte time.
361925
A ball rolls off the top of a staircase with a horizontal velocity \(u\) \(m\)/\(s\). If the steps are \(h\) metre high and \(b\) metre wide, the ball will hit the edge of the \(n\)th step, if:
1 \(n = \frac{{2hu}}{{g{b^2}}}\)
2 \(n = \frac{{2h{u^2}}}{{gb}}\)
3 \(n = \frac{{2h{u^2}}}{{g{b^2}}}\)
4 \(n = \frac{{h{u^2}}}{{g{b^2}}}\)
Explanation:
If the ball hits the nth step, then horizontal distance traversed \( = nh\) Here, velocity along horizontal direction \( = u\) Velocity along vertical direction \( = 0\) \(\therefore \;\;nb = ut\) \(nh = 0 + \frac{1}{2}g{t^2}\) From (1) \(t = \frac{{nb}}{v},\;\therefore nh = \frac{1}{2}g \times {\left( {\frac{{nb}}{u}} \right)^2}\) \(n = \frac{{2h{u^2}}}{{g{b^2}}}\)
PHXI04:MOTION IN A PLANE
361926
A body is projected horizontally with velocity \(196\;m{s^{ - 1}}\) from height \(400\;m.\) What is the time to reach the ground?
361927
A staircase contains three steps each 10 \(cm\) high and 20 \(cm\) wide. What should be the minimum horizontal velocity of the ball rolling off the uppermost plane so as to hit directly the lowest plane?
1 \(7\,m{s^{ - 1}}\)
2 \(2\,m{s^{ - 1}}\)
3 \(4\,m{s^{ - 1}}\)
4 \(10\,m{s^{ - 1}}\)
Explanation:
At minimum velocity, it will move just touching point \(E\) reaching the ground. \(A\) is the origin of reference co-ordinate. If \(u\) is the minimum speed \(\begin{aligned}& x=40, y=20, \theta=0^{\circ} \\& y=\tan \theta-g \dfrac{x^{2} \sec ^{2} \theta}{2 u^{2}}\end{aligned}\) where \(g=10 {~ms}^{-2}\) \(=1000 {~cm} {~s}^{-2}\) \(\begin{aligned}& -20=-\dfrac{800000}{2 u^{2}} \\& u=200 {~cm} {~s}^{-1}=2 {~ms}^{-1}\end{aligned}\)
PHXI04:MOTION IN A PLANE
361928
If a body is projected with an angle \(\theta \) to the horizontal, then
1 Its velocity is always prependicular to its acceleration
2 Its velocity becomes zero at its maximum height
3 Its velocity makes zero angle with the horizontal at its maximum height
4 The body just before hitting the ground, the direction of velocity coincides with the accleration
361924
A ball is projected horizontally from the top of the tower with a velocity \({v_0}\). It will be moving at angle of \(60^\circ \) with the horizontal afte time.
361925
A ball rolls off the top of a staircase with a horizontal velocity \(u\) \(m\)/\(s\). If the steps are \(h\) metre high and \(b\) metre wide, the ball will hit the edge of the \(n\)th step, if:
1 \(n = \frac{{2hu}}{{g{b^2}}}\)
2 \(n = \frac{{2h{u^2}}}{{gb}}\)
3 \(n = \frac{{2h{u^2}}}{{g{b^2}}}\)
4 \(n = \frac{{h{u^2}}}{{g{b^2}}}\)
Explanation:
If the ball hits the nth step, then horizontal distance traversed \( = nh\) Here, velocity along horizontal direction \( = u\) Velocity along vertical direction \( = 0\) \(\therefore \;\;nb = ut\) \(nh = 0 + \frac{1}{2}g{t^2}\) From (1) \(t = \frac{{nb}}{v},\;\therefore nh = \frac{1}{2}g \times {\left( {\frac{{nb}}{u}} \right)^2}\) \(n = \frac{{2h{u^2}}}{{g{b^2}}}\)
PHXI04:MOTION IN A PLANE
361926
A body is projected horizontally with velocity \(196\;m{s^{ - 1}}\) from height \(400\;m.\) What is the time to reach the ground?
361927
A staircase contains three steps each 10 \(cm\) high and 20 \(cm\) wide. What should be the minimum horizontal velocity of the ball rolling off the uppermost plane so as to hit directly the lowest plane?
1 \(7\,m{s^{ - 1}}\)
2 \(2\,m{s^{ - 1}}\)
3 \(4\,m{s^{ - 1}}\)
4 \(10\,m{s^{ - 1}}\)
Explanation:
At minimum velocity, it will move just touching point \(E\) reaching the ground. \(A\) is the origin of reference co-ordinate. If \(u\) is the minimum speed \(\begin{aligned}& x=40, y=20, \theta=0^{\circ} \\& y=\tan \theta-g \dfrac{x^{2} \sec ^{2} \theta}{2 u^{2}}\end{aligned}\) where \(g=10 {~ms}^{-2}\) \(=1000 {~cm} {~s}^{-2}\) \(\begin{aligned}& -20=-\dfrac{800000}{2 u^{2}} \\& u=200 {~cm} {~s}^{-1}=2 {~ms}^{-1}\end{aligned}\)
PHXI04:MOTION IN A PLANE
361928
If a body is projected with an angle \(\theta \) to the horizontal, then
1 Its velocity is always prependicular to its acceleration
2 Its velocity becomes zero at its maximum height
3 Its velocity makes zero angle with the horizontal at its maximum height
4 The body just before hitting the ground, the direction of velocity coincides with the accleration
