tand so that it cannot topple over. The object must be positioned so that it cannot cause injury as it falls. CHECKPOINT Estimate the speed at which a coconut from the tree in fig A would hit the sand. x How fast would a fountain need to squirt its water upwards to reach a height of 15 m? How fast would a snowboarder be moving if he slid down a slope dropping a vertical height of 45 m? ) How high will a 48 kg trampolinist rise if he leaves the trampoline at a speed of 6.1ms^-1 5. What assumption must you make in order to answer all of the above questions?

Question

tand so that it cannot topple over. The object must be positioned so that it cannot cause injury as it falls. CHECKPOINT Estimate the speed at which a coconut from the tree in fig A would hit the sand. x How fast would a fountain need to squirt its water upwards to reach a height of 15 m? How fast would a snowboarder be moving if he slid down a slope dropping a vertical height of 45 m? ) How high will a 48 kg trampolinist rise if he leaves the trampoline at a speed of 6.1ms^-1 5. What assumption must you make in order to answer all of the above questions?

Answer 1

To answer the questions, we need to use the principles of physics, specifically the laws of motion and energy conservation.1. To estimate the speed at which a coconut would hit the sand, we can use the equation for free fall motion: v = sqrt(2gh), where v is the final velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height from which the coconut falls. We need to know the height of the tree to calculate this.2. To find the speed at which a fountain needs to squirt its water upwards to reach a height of 15 m, we can use the equation for vertical motion: v = sqrt(2gh), where v is the initial velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height reached. Solving for v, we get v = sqrt(2 * 9.8 * 15) ≈ 17.1 m/s.3. To find the speed of a snowboarder sliding down a slope dropping a vertical height of 45 m, we can use the equation for conservation of energy: mgh = 0.5mv^2, where m is the mass of the snowboarder, g is the acceleration due to gravity (approximately 9.8 m/s^2), h is the vertical height, and v is the final velocity. Solving for v, we get v = sqrt(2gh) ≈ sqrt(2 * 9.8 * 45) ≈ 30 m/s.4. To find the height a 48 kg trampolinist will rise if he leaves the trampoline at a speed of 6.1 m/s, we can use the equation for conservation of energy: 0.5mv^2 = mgh, where m is the mass of the trampolinist, v is the initial velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height reached. Solving for h, we get h = v^2 / (2g) ≈ (6.1^2) / (2 * 9.8) ≈ 1.9 m.5. The assumption we must make in order to answer all of the above questions is that air resistance is negligible and that the only force acting on the objects is gravity.

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