Question

1. a golf ball is initially at rest sitting on a tee. once hit, it accelerates at a rate of 1.5 m/s² in the horizontal direction until it reaches a final velocity of 15 m/s

a) how long did the golf ball accelerate for?
b) what was the golf balls acceleration in the vertical direction? how do you know?

Explanation:

Step1: Identify the kinematic - equation

We use the equation $v = v_0+at$, where $v$ is final velocity, $v_0$ is initial velocity, $a$ is acceleration and $t$ is time. The golf - ball starts from rest, so $v_0 = 0\ m/s$, $a = 1.5\ m/s^2$ and $v = 15\ m/s$.

Step2: Solve for time $t$

Rearranging the equation $v = v_0+at$ for $t$ (since $v_0 = 0$), we get $t=\frac{v - v_0}{a}=\frac{v}{a}$. Substituting $v = 15\ m/s$ and $a = 1.5\ m/s^2$ into the formula, we have $t=\frac{15}{1.5}$.
$t = 10\ s$

Step3: Analyze vertical acceleration

In the vertical direction, assuming no air - resistance and no other vertical forces acting on the ball during the short time of acceleration on the tee, and considering the normal force and gravitational force balance each other out during the horizontal acceleration phase on the tee. The net vertical force $F_y=0$. According to Newton's second law $F = ma$, if $F_y = 0$, then $a_y=0\ m/s^2$.

Answer:

a) $10\ s$
b) The golf ball's acceleration in the vertical direction is $0\ m/s^2$. We know this because the net vertical force on the ball while it is accelerating horizontally on the tee is zero, according to Newton's second law $F = ma$.