Question

If the ball has a mass of 2.00 kg and is moving at a velocity of 4.50 m/s at point B, what is the height of the hill at point D if the ball is still moving at 1.00 m/s?

Options:
a) 1 m
b) 2 m
c) 3 m
d) 4 m

Answer 1

The height of the hill at point D is 3 m.

Step-by-step explanation:

To calculate the height of the hill at point D, we need to use the conservation of mechanical energy. At point B, the ball has a mass of 2.00 kg and a velocity of 4.50 m/s. At point D, the ball is still moving at 1.00 m/s. We can set up the equation:

Initial kinetic energy + Initial potential energy = Final kinetic energy + Final potential energy

0.5 * (mass) * (velocity at B)^2 + (mass) * g * (height at B) = 0.5 * (mass) * (velocity at D)^2 + (mass) * g * (height at D)

Plugging in the values, we get:

0.5 * 2.00 kg * (4.50 m/s)^2 + 2.00 kg * 9.81 m/s^2 * 0 m = 0.5 * 2.00 kg * (1.00 m/s)^2 + 2.00 kg * 9.81 m/s^2 * (height at D)

Simplifying and solving for the height at D, we get:

height at D = (0.5 * 2.00 kg * (4.50 m/s)^2 - 0.5 * 2.00 kg * (1.00 m/s)^2) / (2.00 kg * 9.81 m/s^2)

height at D = (0.5 * 2.00 kg * 20.25 m^2/s^2 - 0.5 * 2.00 kg * 1.00 m^2/s^2) / (19.62 m/s^2)

height at D = 3.00 m

Therefore, the height of the hill at point D is 3 m.