Classical Mechanics Answers

At a high jump competition, Ashu clears a height of 2.0m. He takes 1.26 s to do the jump (i.e. from the moment he lifts off the ground to when he touches down again).
(i) Sketch a graph showing a variation of the height h/m of the lowest part of his body from the ground with time t/s. Indicate clearly on the graph a few important values of h and corresponding values of t.
(ii) Explain briefly how Ashu’s speed at any height could be determined from the graph.
(iii) Describe the energy changes that take place during the jump.
(iv) In what way is Ashu’s momentum at take-off different from that at touch down. Explain without any calculations.

A spherical balloon is deflated so that its volume is decreasing at a rate of 5 ftଷ/min. How
fast is the diameter of the balloon decreasing when the radius is 3 ft?

When constructing a dam, the bottom of the dam is thicker than the top of the dam. The necessity of having a thick bottom is a result of
1 : the volume of the water behind the dam.
2 : the altitude of the body of water behind the dam.
3 : the depth of the water behind the dam.
4 : the community surrounding the dam

Archimedes' principle states
1 : the volume of an object placed in a liquid is equal to the weight of the liquid that is displaced.
2 : the volume of an object placed in a liquid is equal to the volume of the liquid that is displaced.
3 : an object placed in the fluid loses weight equal to the weight of the liquid that is displaced
4 : the weight of an object placed in a liquid is equal to the weight of the liquid that is displaced

The pressure on a submerged object acts
1 : only on the top surface of the object
2 : perpendicularly on every section of the submerged object
3 : only on the bottom surface of the object.
4 : on the top and the sides of the submerged object

Find the total force on the side of a water-filled tube 2.34 cm high with a radius of 0.300 cm.
1 : 0.506 N
2 : 0.0506 N
3 : 3.41 N
4 : 1.03 N

A rock, initially at rest with respect to Earth and located an infinite distance away is released and accelerates toward Earth. An observation tower is built 3 Earth-radii high to observe the rock as it plummets to Earth. Neglecting friction, how much greater is the rock’s speed when it hits the ground than its speed at the top of the tower?
1 : twice
2 : three times
3 : four times
4 : six times
5 : eight times
6 : nine times
7 : sixteen times

What is the ratio of the escape speed of a rocket launched from sea level to the escape speed of one launched from Mt. Everest (an altitude of {\bf \scriptsize{8.85}}8.85{\bf \scriptsize{8.85}} km)? The radius of the earth is {\bf\scriptsize{6.38 \times 10^6}}6.38×106{\bf\scriptsize{6.38 \times 10^6}} m. (The escape speed is the minimum speed that is required to escape from the influence of the gravitational potential.)
1 : 1.0007
2 : 1.0014
3 : 1.0001
4 : 0.9986
5 : 0.9993

You stand on a spring scale placed on the ground and read your weight from the dial. You then take the scale into an elevator. Does the dial reading increase, decrease, or stay the same when the elevator accelerates downward as it moves upward?
1 : Increase
2 : Decrease
3 : Stay the same

The reason an astronaut in an earth satellite feels weightless is that
1 : the astronaut is beyond the range of the earth's gravity.
2 : the astronaut is falling.
3 : the astronaut is at a point in space where the effects of the moon's gravity and the earth's gravity cancel.
4 : this is a psychological effect associated with rapid motion.
5 : the astronaut's acceleration is zero