Question

A ball is launched with an initial velocity of 44.1 meters per second at an angle of 34.4° above the horizontal. At the peak of its trajectory, what are the components of the ball's velocity vector?

A) 44.1cos(34.4°) m/s horizontally
B) 44.1sin(34.4°) m/s vertically
C) 44.1cos(34.4°) m/s vertically
D) 44.1sin(34.4°) m/s horizontally

Answer 1

At the peak of its trajectory, a ball launched at an angle has a zero vertical velocity component; therefore, the only remaining component is the horizontal one, which is computed using the cosine of the launch angle.

Step-by-step explanation:

At the peak of its trajectory, the velocity vector of a ball launched at an angle above the horizontal will have its vertical component reduced to zero due to gravity. Therefore, the only velocity it retains is the horizontal component, which remains unchanged if we ignore air resistance and other external forces. In this scenario, since the ball was launched with an initial velocity of 44.1 meters per second at an angle of 34.4° above the horizontal, the vertical component of velocity at the peak is zero.

Thus, the ball's velocity components at the peak of its trajectory are:

• 44.1cos(34.4°) m/s horizontally - This is the horizontal component, which remains constant throughout the flight of the projectile.

The correct answer is A) 44.1cos(34.4°) m/s horizontally, because at the peak of its trajectory, the vertical velocity component of the ball is zero due to the force of gravity.