A ball is hit from ground level with a speed of 50 m/s at an angle of 30 degrees

Question

A ball is hit from ground level with a speed of 50 m/s at an angle of 30 degrees above the horizontal. It hits a wall that is 60m from where the ball started. How high up on the wall does the ball hit. Is the ball traveling up or down when it hits the wall? (Show how you conclude this.) A 20 kg child swings in a circle in a carnival ride. The swing is attached to the top of a pole via a rope (as drawn.) The angle between the rope and pole is (yes you guessed it) 30 degrees. Find the tension in the rope. Find the speed of the child. Find the acceleration and the tension in the rope. Include force body diagrams for each block and the appropriate equations.

Explanation / Answer

here,

1)

a)

speed of the ball , v = 50 m/s

theta = 30 degree

distance of wall , x = 60 m

let the height of the the ball hit be y

y = x* tan(theta) - g*x^2/( 2*v^2*cos(theta)^2)

y = 60 * tan(30) - 9.8 * 60^2 /( 2*50^2 * cos(30)^2)

y = 25.23 m

the height on the wall ball hits is 25.23 m

b)

range = v^2*sin(2*theta) /g

range = 50^2*sin(2*30) /9.8

range = 220.92 m

range/2 = 110.46 m

at the time when ball hits the wall , the ball is travelling up as x<R/2

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