A basketball player shoots the ball with an initial velocity of 14.4 ft./sec. at an angle of 41.9° with the horizontal. To the nearest tenth, find the initial horizontal component of the vector that represents the velocity of the ball.

A. 4.8 ft./sec.
B. 5.4 ft./sec.
C. 9.6 ft./sec.
D. 10.7 ft./sec.

1 answer

The initial horizontal component of the velocity can be found using the formula:

v₀x = v₀ * cos(θ)

where:
v₀x = initial horizontal component of the velocity
v₀ = initial velocity (14.4 ft./sec)
θ = angle with the horizontal (41.9°)

Plugging in the values:

v₀x = 14.4 * cos(41.9°)
v₀x = 14.4 * 0.749
v₀x = 10.776

Rounded to the nearest tenth, the initial horizontal component of the vector is 10.8 ft./sec. Therefore, the answer is:

D. 10.7 ft./sec.