Question

a ball is thrown upwards. the vectors represent the velocity of the ball on the way up.
1
2
3
point will have the smallest kinetic energy
point will have the largest momentum

Explanation:

Step1: Recall Kinetic Energy Formula

Kinetic Energy (KE) is given by \( KE = \frac{1}{2}mv^2 \), where \( m \) is mass and \( v \) is speed. For a ball thrown upwards, mass \( m \) is constant. So KE depends on \( v^2 \). The smaller the speed, the smaller the KE. From the vectors, Point 1 has the smallest velocity vector (shortest length), so smallest speed. Thus, Point 1 has smallest KE.

Step2: Recall Momentum Formula

Momentum (\( p \)) is given by \( p = mv \), where \( m \) is mass (constant) and \( v \) is velocity (speed, since direction is same here). Larger speed means larger momentum. Point 3 has the longest velocity vector (largest speed), so largest momentum.

Answer:

• Point 1 will have the smallest Kinetic Energy.
• Point 3 will have the largest Momentum.