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A catapult fires a stone with a speed of u = 7.0 m s¹ from a vertical height of 1.0 m above level ground, as shown in Figure 2. A student tests the device by aiming the stone so that, at its highest point, it just clears a barrier with a height of 3.0 m. The stone then lands in the middle of a frozen pond, whose surface can be assumed to be at the same level as the ground.

A catapult fires a stone with a speed of u = 7.0 m s¹ from a vertical height of 1.0 m above level ground, as shown in Figure 2. A student tests the device by aiming the stone so that, at its highest point, it just clears a barrier with a height of 3.0 m. The stone then lands in the middle of a frozen pond, whose surface can be assumed to be at the same level as the ground.

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In solving this problem, you are advised to take the acceleration due to gravity to be 9.8 m s-2, acting vertically downwards. You should assume that air resistance is negligible and define your coordinate system (x- and y-axes) carefully before tackling the rest of the question. (i) At what angle does the stone need to be launched in order to just clear the barrier? (ii) Show that between its launch and landing, the stone is in the air for 1.4 s. (iii) Use the time that the stone is in the air to calculate the horizontal distance at which the catapult should be positioned from the middle of the pond. (iv) What variables could you alter in order to increase the range of the catapult? No calculation is required for this part of the question.
Transcribed Image Text:In solving this problem, you are advised to take the acceleration due to gravity to be 9.8 m s-2, acting vertically downwards. You should assume that air resistance is negligible and define your coordinate system (x- and y-axes) carefully before tackling the rest of the question. (i) At what angle does the stone need to be launched in order to just clear the barrier? (ii) Show that between its launch and landing, the stone is in the air for 1.4 s. (iii) Use the time that the stone is in the air to calculate the horizontal distance at which the catapult should be positioned from the middle of the pond. (iv) What variables could you alter in order to increase the range of the catapult? No calculation is required for this part of the question.
A catapult fires a stone with a speed of u = 7.0 m s¹ from a vertical height of 1.0 m above level ground, as shown in Figure 2. A student tests the device by aiming the stone so that, at its highest point, it just clears a barrier with a height of 3.0 m. The stone then lands in the middle of a frozen pond, whose surface can be assumed to be at the same level as the ground. 个 1.0m 3.0m Movable barrier ←Pond->
Transcribed Image Text:A catapult fires a stone with a speed of u = 7.0 m s¹ from a vertical height of 1.0 m above level ground, as shown in Figure 2. A student tests the device by aiming the stone so that, at its highest point, it just clears a barrier with a height of 3.0 m. The stone then lands in the middle of a frozen pond, whose surface can be assumed to be at the same level as the ground. 个 1.0m 3.0m Movable barrier ←Pond->
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