Projectile motion

Questions 9 and 10 refer to the information below.

An object was thrown so that it followed the path shown. Assume drag forces were negligible.

The object was thrown with an initial vertical component of velocity u. The time taken to reach maximum height is t.

Which of the following could not be used to determine the maximum vertical height s reached by the object?

In cricket a fielder is often placed at the boundary edge as shown. If the fielder catches the ball, the batter is out.

The fielder is 55.0 m away from the batter. The fielder can catch the ball providing the ball is less than three metres above the height at which it was hit.

The ball is hit with a velocity of 23.8 m s^–1 and at an angle of 50.0 to the horizontal.

Deduce whether the fielder can catch the ball in this case.

The ball was bowled. Just after the bat hit the ball, the ball had a velocity of

Show that the magnitude of the momentum of the ball, after it was hit, was about 3.3 N s.

mass of cricket ball = 0.140 kg

A ball is thrown with an initial horizontal component of velocity u and an initial vertical component of velocity v. The effects of air resistance are negligible.

Which of the following statements about the motion of the ball is not correct?

In the game of golf a stationary ball is hit by a club. One of the aims of the game is to land the ball on a patch of ground called the green.

The graph shows how the force F exerted by the club on the ball varies with time t as the ball is hit.

State why the area under the graph represents impulse.

Show that the velocity of the ball is about 30 m s⁻¹ immediately after it is hit by the club.

mass of ball = 0.046 kg

The ball has a time of flight of 3.5 s before landing. The green is a vertical distance of 7.5 m above the point at which the ball was hit, as shown. The green is about seventy metres away from where the ball is hit.

Deduce whether, if air resistance is ignored, the ball could land on the green after a flight time of 3.5 s.

Scientists have been studying a type of jumping spider that can jump up to six times its body length.

The scientists photographed a spider at 0.02s intervals, during a jump. The picture is taken from the photograph and is shown actual size.

Deduce whether the images show that the motion in the x-direction is independent of the motion in the y-direction. You should take measurements using the cross marking the centre of gravity of the spider.

Show that the initial velocity of the spider at the start of the jump is about 1 m s⁻¹. You should take measurements using the cross marking the centre of gravity of the spider.

The spider achieves this jump by extending its two back legs by 3.0 mm.

Calculate the average force the spider exerts in each leg to achieve the jump.

mass of spider = 150 mg

Just as the spider starts the jump, it fixes a silk thread to the platform. It is thought that the thread acts as a safety line in case the spider falls.

A student makes the comment:

ʻIf the silk thread can withstand a tension equal to the weight of the spider then this safety system should work.ʼ

Deduce whether this statement is correct.

Scientists have been studying a type of jumping spider that can jump up to six times its body length.

The scientists photographed a spider at 0.02s intervals, during a jump. The picture is taken from the photograph and is shown actual size.

Deduce whether the images show that the motion in the x-direction is independent of the motion in the y-direction. You should take measurements using the cross marking the centre of gravity of the spider.

Show that the initial velocity of the spider at the start of the jump is about 1 m s⁻¹. You should take measurements using the cross marking the centre of gravity of the spider.

The spider achieves this jump by extending its two back legs by 3.0 mm.

Calculate the average force the spider exerts in each leg to achieve the jump.

mass of spider = 150 mg

Just as the spider starts the jump, it fixes a silk thread to the platform. It is thought that the thread acts as a safety line in case the spider falls.

A student makes the comment:

ʻIf the silk thread can withstand a tension equal to the weight of the spider then this safety system should work.ʼ

Deduce whether this statement is correct.

A ‘Gauss gun’ can be made from five ball bearings of equal mass and two magnets, as shown.

Pairs of ball bearings are placed to the right of two strong magnets. A single ball bearing is released from the left, as shown. The ball bearing is attracted to, and collides with, the first magnet. This and all subsequent collisions can be assumed to be elastic.

Explain what happens to make the last ball bearing on the right subsequently move off with a large velocity.

A student set up the apparatus shown to measure the speed of the last ball bearing. The ‘Gauss gun’ was placed at the end of a bench, so that the ball bearing left the gun and broke two strips of metal foil which formed part of an electric circuit.

As the ball bearing left the gun, it broke the first foil strip at its centre so that the capacitor started to discharge. When the ball bearing broke the second foil strip the capacitor discharge stopped.

Calculate the energy stored in the capacitor when it was fully charged.

The voltmeter reading halved in the time taken for the ball bearing to travel between the two foil strips.

Show that the time taken for the ball bearing to travel between the two foil strips was about 0.1 s.

The two foil strips were 0.50 m apart.

Calculate the horizontal velocity of the ball bearing.

The student positioned the second foil strip with its centre 8.0 cm lower than the centre of the first foil strip.

Deduce whether the ball bearing broke the second foil strip at its centre.

Assume the ball bearing was travelling horizontally as it broke the first foil strip.

The shot put is an Olympic field event. The distance for the women’s world record shot put is in excess of twenty two metres.

The shot is a metal ball, which is thrown from a standing position so that it lands on the ground a horizontal distance R away from the thrower.

A shot is thrown from a height h above the ground with an initial velocity of 14.2 m s^–1 at an angle of 37.0° to the horizontal. The time it takes for the shot to reach the ground is 1.98 s.

Show that the vertical component of the initial velocity is about 8.6 m s^–1.

Calculate the height h above the ground from which the shot was thrown.

Calculate the horizontal distance R for this throw.