Question

A baseball is projected with a velocity v making an angle θ with the incline of indication α as shown in fig. Find the condition that the ball hits the incline at right angle.

• A. cotθ = tan θ
• B. sin θ = cosα
• C. tanθ = sin α
• D. cot θ = cosα

Answer 1

Answer: (A)

cotθ = tan θ

Answer 2

T = $\frac{2u_{y}}{|a_{y}|} = \frac{2v\sin\theta}{g\cos\alpha}$. It will hit vertically the incline if v_x = 0.

0 = v cos θ T – g sin α T²

or vcos θ$\left( \frac{2v\sin\theta}{g\cos\alpha} \right) - \frac{g\sin\alpha}{2}\left( \frac{2v\sin\theta}{g\cos\alpha} \right)^{2} = 0$

$\frac{2v^{2}\sin\theta}{g\cos\alpha}$ [cos θ cos α - sin α sin θ] = 0

or cot θ = tan α