01. Plane Motion Analysis
Motion in Plane

143704 A block of mass \(1 \mathrm{~kg}\) starts from rest at \(x=0\) and moves along the \(X\)-axis under the action of a force \(F=k t\), where \(t\) is time and \(k=1 N^{-1}\). The distance the block will travel in 6 seconds is

1 \(36 \mathrm{~m}\)
2 \(72 \mathrm{~m}\)
3 \(108 \mathrm{~m}\)
4 \(18 \mathrm{~m}\)
Motion in Plane

143705 A cyclist is moving along a curvature of radius ' \(r\) ' at a constant speed ' \(v\) '. The angle made by the cyclist with the vertical plane is

1 \(\tan ^{-1}\left(\frac{\mathrm{v}^{2}}{\mathrm{rg}}\right)\)
2 \(\tan ^{-1}\left(\frac{\mathrm{rg}}{\mathrm{v}^{2}}\right)\)
3 \(\tan ^{-1}\left(\frac{\mathrm{v}^{2} \mathrm{r}}{\mathrm{g}}\right)\)
4 \(\tan ^{-1}\left(\frac{r}{v^{2} g}\right)\)
Motion in Plane

143706 A boat crosses a river with a velocity of \(8 \mathrm{~km} / h\). If the resulting velocity of boat is \(10 \mathrm{~km} / \mathrm{h}\), then the velocity of river water is

1 \(4 \mathrm{~km} / \mathrm{h}\)
2 \(6 \mathrm{~km} / \mathrm{h}\)
3 \(8 \mathrm{~km} / \mathrm{h}\)
4 \(10 \mathrm{~km} / \mathrm{h}\)
Motion in Plane

143707 An aircraft is flying at a height of ' \(H\) ' above the ground and at a speed of ' \(V\) '. The maximum angle subtended at a ground observation point by the aircraft after time \(T\) is

1 \(\tan ^{-1}\left(\frac{\mathrm{VT}}{\mathrm{H}}\right)\)
2 \(\tan ^{-1}\left(\frac{\mathrm{VT}}{2 \mathrm{H}}\right)\)
3 \(2 \tan ^{-1}\left(\frac{2 \mathrm{VT}}{\mathrm{H}}\right)\)
4 \(2 \tan ^{-1}\left(\frac{\mathrm{VT}}{2 \mathrm{H}}\right)\)
Motion in Plane

143709 Two boys are standing at the ends \(A\) and \(B\) of a ground, where \(A B=a\). The boy at \(B\) starts running in a direction perpendicular to \(A B\) with velocity \(v_{1}\) The boy at \(A\) starts running simultaneously with velocity \(v\) and catches the other boy in a time \(t\), where \(t\) is

1 \(\frac{a}{\sqrt{v^{2}+v_{1}^{2}}}\)
2 \(\sqrt{\frac{a^{2}}{v^{2}-v_{1}^{2}}}\)
3 \(\frac{a}{v-v_{1}}\)
4 \(\frac{a}{v+v_{1}}\)
Motion in Plane

143704 A block of mass \(1 \mathrm{~kg}\) starts from rest at \(x=0\) and moves along the \(X\)-axis under the action of a force \(F=k t\), where \(t\) is time and \(k=1 N^{-1}\). The distance the block will travel in 6 seconds is

1 \(36 \mathrm{~m}\)
2 \(72 \mathrm{~m}\)
3 \(108 \mathrm{~m}\)
4 \(18 \mathrm{~m}\)
Motion in Plane

143705 A cyclist is moving along a curvature of radius ' \(r\) ' at a constant speed ' \(v\) '. The angle made by the cyclist with the vertical plane is

1 \(\tan ^{-1}\left(\frac{\mathrm{v}^{2}}{\mathrm{rg}}\right)\)
2 \(\tan ^{-1}\left(\frac{\mathrm{rg}}{\mathrm{v}^{2}}\right)\)
3 \(\tan ^{-1}\left(\frac{\mathrm{v}^{2} \mathrm{r}}{\mathrm{g}}\right)\)
4 \(\tan ^{-1}\left(\frac{r}{v^{2} g}\right)\)
Motion in Plane

143706 A boat crosses a river with a velocity of \(8 \mathrm{~km} / h\). If the resulting velocity of boat is \(10 \mathrm{~km} / \mathrm{h}\), then the velocity of river water is

1 \(4 \mathrm{~km} / \mathrm{h}\)
2 \(6 \mathrm{~km} / \mathrm{h}\)
3 \(8 \mathrm{~km} / \mathrm{h}\)
4 \(10 \mathrm{~km} / \mathrm{h}\)
Motion in Plane

143707 An aircraft is flying at a height of ' \(H\) ' above the ground and at a speed of ' \(V\) '. The maximum angle subtended at a ground observation point by the aircraft after time \(T\) is

1 \(\tan ^{-1}\left(\frac{\mathrm{VT}}{\mathrm{H}}\right)\)
2 \(\tan ^{-1}\left(\frac{\mathrm{VT}}{2 \mathrm{H}}\right)\)
3 \(2 \tan ^{-1}\left(\frac{2 \mathrm{VT}}{\mathrm{H}}\right)\)
4 \(2 \tan ^{-1}\left(\frac{\mathrm{VT}}{2 \mathrm{H}}\right)\)
Motion in Plane

143709 Two boys are standing at the ends \(A\) and \(B\) of a ground, where \(A B=a\). The boy at \(B\) starts running in a direction perpendicular to \(A B\) with velocity \(v_{1}\) The boy at \(A\) starts running simultaneously with velocity \(v\) and catches the other boy in a time \(t\), where \(t\) is

1 \(\frac{a}{\sqrt{v^{2}+v_{1}^{2}}}\)
2 \(\sqrt{\frac{a^{2}}{v^{2}-v_{1}^{2}}}\)
3 \(\frac{a}{v-v_{1}}\)
4 \(\frac{a}{v+v_{1}}\)
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Motion in Plane

143704 A block of mass \(1 \mathrm{~kg}\) starts from rest at \(x=0\) and moves along the \(X\)-axis under the action of a force \(F=k t\), where \(t\) is time and \(k=1 N^{-1}\). The distance the block will travel in 6 seconds is

1 \(36 \mathrm{~m}\)
2 \(72 \mathrm{~m}\)
3 \(108 \mathrm{~m}\)
4 \(18 \mathrm{~m}\)
Motion in Plane

143705 A cyclist is moving along a curvature of radius ' \(r\) ' at a constant speed ' \(v\) '. The angle made by the cyclist with the vertical plane is

1 \(\tan ^{-1}\left(\frac{\mathrm{v}^{2}}{\mathrm{rg}}\right)\)
2 \(\tan ^{-1}\left(\frac{\mathrm{rg}}{\mathrm{v}^{2}}\right)\)
3 \(\tan ^{-1}\left(\frac{\mathrm{v}^{2} \mathrm{r}}{\mathrm{g}}\right)\)
4 \(\tan ^{-1}\left(\frac{r}{v^{2} g}\right)\)
Motion in Plane

143706 A boat crosses a river with a velocity of \(8 \mathrm{~km} / h\). If the resulting velocity of boat is \(10 \mathrm{~km} / \mathrm{h}\), then the velocity of river water is

1 \(4 \mathrm{~km} / \mathrm{h}\)
2 \(6 \mathrm{~km} / \mathrm{h}\)
3 \(8 \mathrm{~km} / \mathrm{h}\)
4 \(10 \mathrm{~km} / \mathrm{h}\)
Motion in Plane

143707 An aircraft is flying at a height of ' \(H\) ' above the ground and at a speed of ' \(V\) '. The maximum angle subtended at a ground observation point by the aircraft after time \(T\) is

1 \(\tan ^{-1}\left(\frac{\mathrm{VT}}{\mathrm{H}}\right)\)
2 \(\tan ^{-1}\left(\frac{\mathrm{VT}}{2 \mathrm{H}}\right)\)
3 \(2 \tan ^{-1}\left(\frac{2 \mathrm{VT}}{\mathrm{H}}\right)\)
4 \(2 \tan ^{-1}\left(\frac{\mathrm{VT}}{2 \mathrm{H}}\right)\)
Motion in Plane

143709 Two boys are standing at the ends \(A\) and \(B\) of a ground, where \(A B=a\). The boy at \(B\) starts running in a direction perpendicular to \(A B\) with velocity \(v_{1}\) The boy at \(A\) starts running simultaneously with velocity \(v\) and catches the other boy in a time \(t\), where \(t\) is

1 \(\frac{a}{\sqrt{v^{2}+v_{1}^{2}}}\)
2 \(\sqrt{\frac{a^{2}}{v^{2}-v_{1}^{2}}}\)
3 \(\frac{a}{v-v_{1}}\)
4 \(\frac{a}{v+v_{1}}\)
Motion in Plane

143704 A block of mass \(1 \mathrm{~kg}\) starts from rest at \(x=0\) and moves along the \(X\)-axis under the action of a force \(F=k t\), where \(t\) is time and \(k=1 N^{-1}\). The distance the block will travel in 6 seconds is

1 \(36 \mathrm{~m}\)
2 \(72 \mathrm{~m}\)
3 \(108 \mathrm{~m}\)
4 \(18 \mathrm{~m}\)
Motion in Plane

143705 A cyclist is moving along a curvature of radius ' \(r\) ' at a constant speed ' \(v\) '. The angle made by the cyclist with the vertical plane is

1 \(\tan ^{-1}\left(\frac{\mathrm{v}^{2}}{\mathrm{rg}}\right)\)
2 \(\tan ^{-1}\left(\frac{\mathrm{rg}}{\mathrm{v}^{2}}\right)\)
3 \(\tan ^{-1}\left(\frac{\mathrm{v}^{2} \mathrm{r}}{\mathrm{g}}\right)\)
4 \(\tan ^{-1}\left(\frac{r}{v^{2} g}\right)\)
Motion in Plane

143706 A boat crosses a river with a velocity of \(8 \mathrm{~km} / h\). If the resulting velocity of boat is \(10 \mathrm{~km} / \mathrm{h}\), then the velocity of river water is

1 \(4 \mathrm{~km} / \mathrm{h}\)
2 \(6 \mathrm{~km} / \mathrm{h}\)
3 \(8 \mathrm{~km} / \mathrm{h}\)
4 \(10 \mathrm{~km} / \mathrm{h}\)
Motion in Plane

143707 An aircraft is flying at a height of ' \(H\) ' above the ground and at a speed of ' \(V\) '. The maximum angle subtended at a ground observation point by the aircraft after time \(T\) is

1 \(\tan ^{-1}\left(\frac{\mathrm{VT}}{\mathrm{H}}\right)\)
2 \(\tan ^{-1}\left(\frac{\mathrm{VT}}{2 \mathrm{H}}\right)\)
3 \(2 \tan ^{-1}\left(\frac{2 \mathrm{VT}}{\mathrm{H}}\right)\)
4 \(2 \tan ^{-1}\left(\frac{\mathrm{VT}}{2 \mathrm{H}}\right)\)
Motion in Plane

143709 Two boys are standing at the ends \(A\) and \(B\) of a ground, where \(A B=a\). The boy at \(B\) starts running in a direction perpendicular to \(A B\) with velocity \(v_{1}\) The boy at \(A\) starts running simultaneously with velocity \(v\) and catches the other boy in a time \(t\), where \(t\) is

1 \(\frac{a}{\sqrt{v^{2}+v_{1}^{2}}}\)
2 \(\sqrt{\frac{a^{2}}{v^{2}-v_{1}^{2}}}\)
3 \(\frac{a}{v-v_{1}}\)
4 \(\frac{a}{v+v_{1}}\)
Motion in Plane

143704 A block of mass \(1 \mathrm{~kg}\) starts from rest at \(x=0\) and moves along the \(X\)-axis under the action of a force \(F=k t\), where \(t\) is time and \(k=1 N^{-1}\). The distance the block will travel in 6 seconds is

1 \(36 \mathrm{~m}\)
2 \(72 \mathrm{~m}\)
3 \(108 \mathrm{~m}\)
4 \(18 \mathrm{~m}\)
Motion in Plane

143705 A cyclist is moving along a curvature of radius ' \(r\) ' at a constant speed ' \(v\) '. The angle made by the cyclist with the vertical plane is

1 \(\tan ^{-1}\left(\frac{\mathrm{v}^{2}}{\mathrm{rg}}\right)\)
2 \(\tan ^{-1}\left(\frac{\mathrm{rg}}{\mathrm{v}^{2}}\right)\)
3 \(\tan ^{-1}\left(\frac{\mathrm{v}^{2} \mathrm{r}}{\mathrm{g}}\right)\)
4 \(\tan ^{-1}\left(\frac{r}{v^{2} g}\right)\)
Motion in Plane

143706 A boat crosses a river with a velocity of \(8 \mathrm{~km} / h\). If the resulting velocity of boat is \(10 \mathrm{~km} / \mathrm{h}\), then the velocity of river water is

1 \(4 \mathrm{~km} / \mathrm{h}\)
2 \(6 \mathrm{~km} / \mathrm{h}\)
3 \(8 \mathrm{~km} / \mathrm{h}\)
4 \(10 \mathrm{~km} / \mathrm{h}\)
Motion in Plane

143707 An aircraft is flying at a height of ' \(H\) ' above the ground and at a speed of ' \(V\) '. The maximum angle subtended at a ground observation point by the aircraft after time \(T\) is

1 \(\tan ^{-1}\left(\frac{\mathrm{VT}}{\mathrm{H}}\right)\)
2 \(\tan ^{-1}\left(\frac{\mathrm{VT}}{2 \mathrm{H}}\right)\)
3 \(2 \tan ^{-1}\left(\frac{2 \mathrm{VT}}{\mathrm{H}}\right)\)
4 \(2 \tan ^{-1}\left(\frac{\mathrm{VT}}{2 \mathrm{H}}\right)\)
Motion in Plane

143709 Two boys are standing at the ends \(A\) and \(B\) of a ground, where \(A B=a\). The boy at \(B\) starts running in a direction perpendicular to \(A B\) with velocity \(v_{1}\) The boy at \(A\) starts running simultaneously with velocity \(v\) and catches the other boy in a time \(t\), where \(t\) is

1 \(\frac{a}{\sqrt{v^{2}+v_{1}^{2}}}\)
2 \(\sqrt{\frac{a^{2}}{v^{2}-v_{1}^{2}}}\)
3 \(\frac{a}{v-v_{1}}\)
4 \(\frac{a}{v+v_{1}}\)