Question

a ball of mass m is thrown with an initial speed of u at an angle θ to the horizontal as shown. q is the highest point of the motion. air resistance is negligible. what is the momentum of the ball at q? a. zero b. mu cosθ c. mu d. mu sinθ

Explanation:

Step1: Analyze velocity at highest point

In projectile - motion, at the highest point \(Q\), the vertical component of velocity \(v_y = 0\). The horizontal component of the initial velocity \(u_x=u\cos\theta\), and since there is no acceleration in the horizontal direction (air - resistance is negligible), the horizontal component of velocity remains constant throughout the motion. So, the velocity of the ball at the highest point \(v = u\cos\theta\).

Step2: Recall momentum formula

The momentum of an object is given by \(p = mv\), where \(m\) is the mass of the object and \(v\) is its velocity.

Step3: Calculate momentum at Q

Substitute \(v = u\cos\theta\) into the momentum formula. We get \(p=m\times u\cos\theta=mu\cos\theta\).

Answer:

B. \(mu\cos\theta\)