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…
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
Answer
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)