A wizard places a cannon on the surface of a distant planet that has the gravita

Question

A wizard places a cannon on the surface of a distant planet that has the gravitational Force of half of earth's. A 50kg ball is fired from the cannon at 48 degrees from the horizontal. The ball reaches a height of 255m. Calculate the magnitude of the ball's initial velocity, the time it spends in the air, and how far the ball travels horizontally. Now suppose the wizard then reduces the gravity to a fourth of that of earth's and has the ball fired at an angle of 60 degrees from the horizontal. How much higher would it travel if it were fired from the same initial velocity?

Explanation / Answer

Data: Mass, m = 50 kg Angle, = 48 deg Height, H = 255 m Acceleration due to gravity, g = 9.8 / 2                                                    = 4.9 m/s^2 [ half of the earth ] Solution: (a) H = ( v sin )^2 / 2 g v = ( 2 g H ) / sin    = ( 2 * 4.9 * 255 ) / sin 48    = 67.27 m/s Ans: Initial speed, v = 67.27 m/s (b) Time of flight, T = 2 v sin / g                              = 2 * 67.27 * sin 48 / 4.9                              = 20.4 s Ans: Time of flight, T = 20.4 s (c) Horizontal range, R = v^2 sin 2 / g                                    = 67.27^2 * sin 96 / 4.9                                    = 918.5 m Ans: Horizontal distance, R = 918.5 m (d) Acceleration due to gravity, g = 9.8 / 4                                                    = 2.45 m/s^2 Angle, = 60 deg Velocity, v = 67.27 m/s Height, H = ( v sin )^2 / 2 g                   = ( 67.27 * sin 60 )^2 / ( 2 * 2.45 )                   = 692.6 m Ans: Height, H = 692.6 m

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