# A man stands on the roof of a building of height 13.7m and throws a rock with a velocity of magnitude 28.0m/s at an angle of 27.5 degrees above the horizontal.A. calculate the maximum height...

A man stands on the roof of a building of height 13.7m and throws a rock with a velocity of magnitude 28.0m/s at an angle of 27.5 degrees above the horizontal.

A. calculate the maximum height above the roof reached by the rock. **Answer in m**

B. Calculate the magnitude of the velocity of the rock just before it strikes ground. **Answer in m/s**

C. Calculate the horizontal distance from the base of the building to the point where the rock strikes the ground. **Answer in m**

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### 1 Answer

A man stands on the roof of a building of height 13.7 m and throws a rock with a velocity of magnitude 28.0 m/s at an angle of 27.5 degrees above the horizontal.

The maximum height that the projectile reaches is given by (v*sin x)^2/2*g where v is the initial velocity and x is the angle made with the horizontal. Substituting the values from the problem the maximum height is (28*sin 27.5)^2/19.6 = 8.528 m. But the rock is thrown from the top of a building at a height of 13.7 m. This gives the maximum height as 22.22 m

The magnitude of the velocity when it completes the projectile path and reaches the height it was thrown from is 28.0 m/s at an angle of 27.5 degrees with the horizontal. Here, the horizontal component of the velocity is 28*cos 27.5 = 24.5 m/s The vertical component is 28*sin 27.5, but as the rock falls another 13.7 m it increases to v, where v^2 = (28*sin 27.5)^2 + 2*9.8*13.7 = 20.87 m/s . The magnitude of the velocity is sqrt(20.887^2 + 24.5^2) = 32.19 m/s

The range of the rock till it reaches the height it was thrown from is v^2*(sin 2x)/g = 65.53 m. The time taken by the rock to fall 13.7 m is t where 13.7 = 28*sin 27.5*t + (1/2)*9.8*t^2

Solving, the equation t = 0.6070 s. IN this time the horizontal distance covered is 24.5*0.6070 = 14.88 m

This gives the distance from the base of the building where the rock hits the ground as 80.41 m

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