A stone is thrown with an initial speed of 15 m/s at an angle of 53 $\degree$ above the horizontal from the top of a 35 m building.If g = 9.8 m/s² and air resistance is negligible,then what is the magnitude of the horizontal component of velocity as the rock strikes the ground? A)7.5 m/s B)9.0 m/s C)12 m/s D)29 m/s

Question

Quizplus · Accepted Answer

We can break the initial velocity into its horizontal and vertical components:
v_x = v_initial cosθ = 15 cos53° = 9.9 m/s
v_y = v_initial sinθ = 15 sin53° = 12.1 m/s

Using the formula y = y_initial + v_initialt + 1/2at^2, we can find the time it takes for the stone to fall to the ground:
0 = 35 + 12.1t - 4.9t^2
Solving for t, we get t = 3.54 s

The horizontal distance the stone travels is simply:
x = v_xt = (9.9 m/s)(3.54 s) = 35.1 m

Therefore, the magnitude of the horizontal component of velocity as the rock strikes the ground is 9.9 m/s, which is option B.

A Stone Is Thrown with an Initial Speed of 15 °\degree°

A Stone Is Thrown with an Initial Speed of 15 $\degree$