If Emily throws the ball at an angle of 30∘ below the horizontal with a speed...

If Emily throws the ball at an angle of 30∘ below the horizontal with a speed of 14m/s, how far from the base of the dorm should Allison stand to catch the ball? Assume the vertical distance between where Emily releases the ball and Allison catches it is 8.0m.

Solutions

Expert Solution

Let us consider the downwards direction as positive.

Gravitational acceleration = g = 9.81 m/s²

Initial velocity of the ball = V = 14 m/s

Angle the ball is thrown at = = 30^o below the horizontal

Initial horizontal velocity of the ball = V_x = VCos = (14)Cos(30) = 12.12 m/s

Initial vertical velocity of the ball = V_y = VSin = (14)Sin(30) = 7 m/s

Vertical distance between where Emily releases the ball and Allison catches it = H = 8 m

Time taken by the ball to reach Allison = T

T = 0.749 sec or -2.18 sec

Time cannot be negative.

T = 0.749 sec

Horizontal distance traveled by the ball = R

There is no horizontal force acting on the ball therefore the horizontal velocity of the ball remains constant.

R = V_xT

R = (12.12)(0.749)

R = 9.08 m

Distance from the base of the dorm Allison should stand to catch the ball = 9.08 m

genius_generous answered 1 year ago

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