A ball of 0.2 kg hits a wall with a velocity of 25 m/s at an angle of 45°. If the ball rebounds at 90° to the direction of incidence, change in momentum of the ball -
Question
A ball of 0.2 kg hits a wall with a velocity of 25 m/s at an angle of 45°. If the ball rebounds at 90° to the direction of incidence, change in momentum of the ball -
Solution
To find the change in momentum of the ball, we can use the principle of conservation of momentum.
Step 1: Calculate the initial momentum of the ball before the collision. The initial momentum (p_initial) can be calculated using the formula: p_initial = mass * velocity
Given that the mass of the ball is 0.2 kg and the velocity is 25 m/s, we can substitute these values into the formula: p_initial = 0.2 kg * 25 m/s
Step 2: Calculate the final momentum of the ball after the collision. Since the ball rebounds at 90° to the direction of incidence, the final momentum (p_final) will have the same magnitude as the initial momentum but in the opposite direction.
Therefore, the final momentum can be calculated as: p_final = -p_initial
Step 3: Calculate the change in momentum. The change in momentum (Δp) can be calculated by subtracting the initial momentum from the final momentum: Δp = p_final - p_initial
Substituting the values we calculated earlier: Δp = (-p_initial) - p_initial
Simplifying the equation: Δp = -2 * p_initial
Now, we can substitute the value of p_initial into the equation: Δp = -2 * (0.2 kg * 25 m/s)
Calculating the change in momentum: Δp = -2 * 5 kg m/s
Therefore, the change in momentum of the ball is -10 kg m/s.
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