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 ball’s acceleration in the vertical direction? how do you know?

Explanation:

Step1: Identify the formula

We use the formula $v = u+at$, where $v$ is final - velocity, $u$ is initial - velocity, $a$ is acceleration and $t$ is time. The initial velocity $u = 0\ m/s$ (initially at rest), $v = 15\ m/s$ and $a = 1.5\ m/s^{2}$.

Step2: Rearrange the formula for time

From $v = u + at$, we can solve for $t$ as $t=\frac{v - u}{a}$. Substituting the values: $t=\frac{15 - 0}{1.5}$.

Step3: Calculate the time

$t=\frac{15}{1.5}=10\ s$.

For part b:
The golf - ball is initially at rest on a tee and there is no force acting on it in the vertical direction immediately after it is hit (assuming no air - resistance or other vertical forces). According to Newton's first law (an object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force), the acceleration in the vertical direction $a_y=0\ m/s^{2}$ because there is no net vertical force acting on the ball at the moment of hitting (neglecting air - resistance and other vertical forces).

Answer:

a) $10\ s$
b) $0\ m/s^{2}$. There is no net vertical force acting on the ball immediately after it is hit (neglecting air - resistance and other vertical forces), so according to Newton's first law, the acceleration in the vertical direction is $0\ m/s^{2}$.