02. Relative Velocity in One Dimension
Motion in One Dimensions

141651 A train of \(150 \mathrm{~m}\) length is going towards north direction at a speed of \(10 \mathrm{~ms}^{-1}\). A parrot flies at speed at \(5 \mathrm{~ms}^{-1}\) towards south direction parallel to the railway track. The time taken by the parrot to cross the train is equal to:

1 \(12 \mathrm{~s}\)
2 \(8 \mathrm{~s}\)
3 \(15 \mathrm{~s}\)
4 \(10 \mathrm{~s}\)
5 \(5 \mathrm{~s}\)
Motion in One Dimensions

141652 A police van moving on a highway with a speed of \(30 \mathrm{~km} \mathrm{~h}^{-1}\) fires a bullet at a thief's car speeding away in the same direction with a speed of \(192 \mathrm{~km} \mathrm{~h}^{-1}\). If the muzzle speed of the bullet is \(150 \mathrm{~m} \mathrm{~s}^{-1}\), with what speed does the bullet hit the thief's car?

1 \(90 \mathrm{~m} \mathrm{~s}^{-1}\)
2 \(105 \mathrm{~m} \mathrm{~s}^{-1}\)
3 \(110 \mathrm{~m} \mathrm{~s}^{-1}\)
4 \(120 \mathrm{~m} \mathrm{~s}^{-1}\)
Motion in One Dimensions

141653 A man of height \(h\) walks in a straight path towards a lamp post of height \(H\) with uniform velocity \(u\). Then the velocity of the edge of the shadow on the ground will be:

1 \(\frac{\mathrm{Hu}}{(\mathrm{H}-\mathrm{h})}\)
2 \(\frac{\mathrm{Hu}}{(\mathrm{H}+\mathrm{h})}\)
3 \(\frac{(\mathrm{H}-\mathrm{h})}{\mathrm{Hu}}\)
4 \(\frac{(\mathrm{H}+\mathrm{h})}{\mathrm{Hu}}\)
5 \(\left(\frac{H+h}{H-h}\right) u\)
Motion in One Dimensions

141654 Two trains \(A\) and \(B\) of length \(400 \mathrm{~m}\) each are moving on two parallel tracks with a uniform speed of \(72 \mathrm{kmh}^{-1}\) in the same direction, with \(A\) head of speed \(B\). The driver of \(B\) decides to overtake \(A\) and accelerates by \(1 \mathrm{~m} / \mathrm{s}^{2}\). If after 50s, the guard of \(B\) just brushes past the driver of \(A\), what was the original distance between them?

1 \(100 \mathrm{~m}\)
2 \(1150 \mathrm{~m}\)
3 \(1300 \mathrm{~m}\)
4 \(1250 \mathrm{~m}\)
Motion in One Dimensions

141656 The angle made by \(\overrightarrow{\mathrm{r}}=3 \overrightarrow{\mathrm{i}}+3 \overrightarrow{\mathrm{j}}\) with the \(\mathrm{x}\) axis is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(180^{\circ}\)
4 \(90^{\circ}\)
5 \(45^{\circ}\)
Motion in One Dimensions

141651 A train of \(150 \mathrm{~m}\) length is going towards north direction at a speed of \(10 \mathrm{~ms}^{-1}\). A parrot flies at speed at \(5 \mathrm{~ms}^{-1}\) towards south direction parallel to the railway track. The time taken by the parrot to cross the train is equal to:

1 \(12 \mathrm{~s}\)
2 \(8 \mathrm{~s}\)
3 \(15 \mathrm{~s}\)
4 \(10 \mathrm{~s}\)
5 \(5 \mathrm{~s}\)
Motion in One Dimensions

141652 A police van moving on a highway with a speed of \(30 \mathrm{~km} \mathrm{~h}^{-1}\) fires a bullet at a thief's car speeding away in the same direction with a speed of \(192 \mathrm{~km} \mathrm{~h}^{-1}\). If the muzzle speed of the bullet is \(150 \mathrm{~m} \mathrm{~s}^{-1}\), with what speed does the bullet hit the thief's car?

1 \(90 \mathrm{~m} \mathrm{~s}^{-1}\)
2 \(105 \mathrm{~m} \mathrm{~s}^{-1}\)
3 \(110 \mathrm{~m} \mathrm{~s}^{-1}\)
4 \(120 \mathrm{~m} \mathrm{~s}^{-1}\)
Motion in One Dimensions

141653 A man of height \(h\) walks in a straight path towards a lamp post of height \(H\) with uniform velocity \(u\). Then the velocity of the edge of the shadow on the ground will be:

1 \(\frac{\mathrm{Hu}}{(\mathrm{H}-\mathrm{h})}\)
2 \(\frac{\mathrm{Hu}}{(\mathrm{H}+\mathrm{h})}\)
3 \(\frac{(\mathrm{H}-\mathrm{h})}{\mathrm{Hu}}\)
4 \(\frac{(\mathrm{H}+\mathrm{h})}{\mathrm{Hu}}\)
5 \(\left(\frac{H+h}{H-h}\right) u\)
Motion in One Dimensions

141654 Two trains \(A\) and \(B\) of length \(400 \mathrm{~m}\) each are moving on two parallel tracks with a uniform speed of \(72 \mathrm{kmh}^{-1}\) in the same direction, with \(A\) head of speed \(B\). The driver of \(B\) decides to overtake \(A\) and accelerates by \(1 \mathrm{~m} / \mathrm{s}^{2}\). If after 50s, the guard of \(B\) just brushes past the driver of \(A\), what was the original distance between them?

1 \(100 \mathrm{~m}\)
2 \(1150 \mathrm{~m}\)
3 \(1300 \mathrm{~m}\)
4 \(1250 \mathrm{~m}\)
Motion in One Dimensions

141656 The angle made by \(\overrightarrow{\mathrm{r}}=3 \overrightarrow{\mathrm{i}}+3 \overrightarrow{\mathrm{j}}\) with the \(\mathrm{x}\) axis is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(180^{\circ}\)
4 \(90^{\circ}\)
5 \(45^{\circ}\)
Motion in One Dimensions

141651 A train of \(150 \mathrm{~m}\) length is going towards north direction at a speed of \(10 \mathrm{~ms}^{-1}\). A parrot flies at speed at \(5 \mathrm{~ms}^{-1}\) towards south direction parallel to the railway track. The time taken by the parrot to cross the train is equal to:

1 \(12 \mathrm{~s}\)
2 \(8 \mathrm{~s}\)
3 \(15 \mathrm{~s}\)
4 \(10 \mathrm{~s}\)
5 \(5 \mathrm{~s}\)
Motion in One Dimensions

141652 A police van moving on a highway with a speed of \(30 \mathrm{~km} \mathrm{~h}^{-1}\) fires a bullet at a thief's car speeding away in the same direction with a speed of \(192 \mathrm{~km} \mathrm{~h}^{-1}\). If the muzzle speed of the bullet is \(150 \mathrm{~m} \mathrm{~s}^{-1}\), with what speed does the bullet hit the thief's car?

1 \(90 \mathrm{~m} \mathrm{~s}^{-1}\)
2 \(105 \mathrm{~m} \mathrm{~s}^{-1}\)
3 \(110 \mathrm{~m} \mathrm{~s}^{-1}\)
4 \(120 \mathrm{~m} \mathrm{~s}^{-1}\)
Motion in One Dimensions

141653 A man of height \(h\) walks in a straight path towards a lamp post of height \(H\) with uniform velocity \(u\). Then the velocity of the edge of the shadow on the ground will be:

1 \(\frac{\mathrm{Hu}}{(\mathrm{H}-\mathrm{h})}\)
2 \(\frac{\mathrm{Hu}}{(\mathrm{H}+\mathrm{h})}\)
3 \(\frac{(\mathrm{H}-\mathrm{h})}{\mathrm{Hu}}\)
4 \(\frac{(\mathrm{H}+\mathrm{h})}{\mathrm{Hu}}\)
5 \(\left(\frac{H+h}{H-h}\right) u\)
Motion in One Dimensions

141654 Two trains \(A\) and \(B\) of length \(400 \mathrm{~m}\) each are moving on two parallel tracks with a uniform speed of \(72 \mathrm{kmh}^{-1}\) in the same direction, with \(A\) head of speed \(B\). The driver of \(B\) decides to overtake \(A\) and accelerates by \(1 \mathrm{~m} / \mathrm{s}^{2}\). If after 50s, the guard of \(B\) just brushes past the driver of \(A\), what was the original distance between them?

1 \(100 \mathrm{~m}\)
2 \(1150 \mathrm{~m}\)
3 \(1300 \mathrm{~m}\)
4 \(1250 \mathrm{~m}\)
Motion in One Dimensions

141656 The angle made by \(\overrightarrow{\mathrm{r}}=3 \overrightarrow{\mathrm{i}}+3 \overrightarrow{\mathrm{j}}\) with the \(\mathrm{x}\) axis is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(180^{\circ}\)
4 \(90^{\circ}\)
5 \(45^{\circ}\)
Motion in One Dimensions

141651 A train of \(150 \mathrm{~m}\) length is going towards north direction at a speed of \(10 \mathrm{~ms}^{-1}\). A parrot flies at speed at \(5 \mathrm{~ms}^{-1}\) towards south direction parallel to the railway track. The time taken by the parrot to cross the train is equal to:

1 \(12 \mathrm{~s}\)
2 \(8 \mathrm{~s}\)
3 \(15 \mathrm{~s}\)
4 \(10 \mathrm{~s}\)
5 \(5 \mathrm{~s}\)
Motion in One Dimensions

141652 A police van moving on a highway with a speed of \(30 \mathrm{~km} \mathrm{~h}^{-1}\) fires a bullet at a thief's car speeding away in the same direction with a speed of \(192 \mathrm{~km} \mathrm{~h}^{-1}\). If the muzzle speed of the bullet is \(150 \mathrm{~m} \mathrm{~s}^{-1}\), with what speed does the bullet hit the thief's car?

1 \(90 \mathrm{~m} \mathrm{~s}^{-1}\)
2 \(105 \mathrm{~m} \mathrm{~s}^{-1}\)
3 \(110 \mathrm{~m} \mathrm{~s}^{-1}\)
4 \(120 \mathrm{~m} \mathrm{~s}^{-1}\)
Motion in One Dimensions

141653 A man of height \(h\) walks in a straight path towards a lamp post of height \(H\) with uniform velocity \(u\). Then the velocity of the edge of the shadow on the ground will be:

1 \(\frac{\mathrm{Hu}}{(\mathrm{H}-\mathrm{h})}\)
2 \(\frac{\mathrm{Hu}}{(\mathrm{H}+\mathrm{h})}\)
3 \(\frac{(\mathrm{H}-\mathrm{h})}{\mathrm{Hu}}\)
4 \(\frac{(\mathrm{H}+\mathrm{h})}{\mathrm{Hu}}\)
5 \(\left(\frac{H+h}{H-h}\right) u\)
Motion in One Dimensions

141654 Two trains \(A\) and \(B\) of length \(400 \mathrm{~m}\) each are moving on two parallel tracks with a uniform speed of \(72 \mathrm{kmh}^{-1}\) in the same direction, with \(A\) head of speed \(B\). The driver of \(B\) decides to overtake \(A\) and accelerates by \(1 \mathrm{~m} / \mathrm{s}^{2}\). If after 50s, the guard of \(B\) just brushes past the driver of \(A\), what was the original distance between them?

1 \(100 \mathrm{~m}\)
2 \(1150 \mathrm{~m}\)
3 \(1300 \mathrm{~m}\)
4 \(1250 \mathrm{~m}\)
Motion in One Dimensions

141656 The angle made by \(\overrightarrow{\mathrm{r}}=3 \overrightarrow{\mathrm{i}}+3 \overrightarrow{\mathrm{j}}\) with the \(\mathrm{x}\) axis is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(180^{\circ}\)
4 \(90^{\circ}\)
5 \(45^{\circ}\)
Motion in One Dimensions

141651 A train of \(150 \mathrm{~m}\) length is going towards north direction at a speed of \(10 \mathrm{~ms}^{-1}\). A parrot flies at speed at \(5 \mathrm{~ms}^{-1}\) towards south direction parallel to the railway track. The time taken by the parrot to cross the train is equal to:

1 \(12 \mathrm{~s}\)
2 \(8 \mathrm{~s}\)
3 \(15 \mathrm{~s}\)
4 \(10 \mathrm{~s}\)
5 \(5 \mathrm{~s}\)
Motion in One Dimensions

141652 A police van moving on a highway with a speed of \(30 \mathrm{~km} \mathrm{~h}^{-1}\) fires a bullet at a thief's car speeding away in the same direction with a speed of \(192 \mathrm{~km} \mathrm{~h}^{-1}\). If the muzzle speed of the bullet is \(150 \mathrm{~m} \mathrm{~s}^{-1}\), with what speed does the bullet hit the thief's car?

1 \(90 \mathrm{~m} \mathrm{~s}^{-1}\)
2 \(105 \mathrm{~m} \mathrm{~s}^{-1}\)
3 \(110 \mathrm{~m} \mathrm{~s}^{-1}\)
4 \(120 \mathrm{~m} \mathrm{~s}^{-1}\)
Motion in One Dimensions

141653 A man of height \(h\) walks in a straight path towards a lamp post of height \(H\) with uniform velocity \(u\). Then the velocity of the edge of the shadow on the ground will be:

1 \(\frac{\mathrm{Hu}}{(\mathrm{H}-\mathrm{h})}\)
2 \(\frac{\mathrm{Hu}}{(\mathrm{H}+\mathrm{h})}\)
3 \(\frac{(\mathrm{H}-\mathrm{h})}{\mathrm{Hu}}\)
4 \(\frac{(\mathrm{H}+\mathrm{h})}{\mathrm{Hu}}\)
5 \(\left(\frac{H+h}{H-h}\right) u\)
Motion in One Dimensions

141654 Two trains \(A\) and \(B\) of length \(400 \mathrm{~m}\) each are moving on two parallel tracks with a uniform speed of \(72 \mathrm{kmh}^{-1}\) in the same direction, with \(A\) head of speed \(B\). The driver of \(B\) decides to overtake \(A\) and accelerates by \(1 \mathrm{~m} / \mathrm{s}^{2}\). If after 50s, the guard of \(B\) just brushes past the driver of \(A\), what was the original distance between them?

1 \(100 \mathrm{~m}\)
2 \(1150 \mathrm{~m}\)
3 \(1300 \mathrm{~m}\)
4 \(1250 \mathrm{~m}\)
Motion in One Dimensions

141656 The angle made by \(\overrightarrow{\mathrm{r}}=3 \overrightarrow{\mathrm{i}}+3 \overrightarrow{\mathrm{j}}\) with the \(\mathrm{x}\) axis is

1 \(30^{\circ}\)
2 \(60^{\circ}\)
3 \(180^{\circ}\)
4 \(90^{\circ}\)
5 \(45^{\circ}\)