Question

You are playing miniature golf at the golf course shown in

FIGURE P2.51. Due to the fake plastic grass, the ball decelerates at 1.0 m/s2 when rolling horizontally and at 6.0 m/s2 on the slope. What is the slowest speed with which the ball can leave your golf club if you wish to make a hole in one?

Short answer

The slowest speed with which the ball can leave the golf club is$5.7m/s.$

Step-by-step solution

Given information

The magnitude of acceleration of the ball while rolling horizontally is, $a_1=1m/s^2.$

The magnitude of acceleration of the the ball on the slope is, role="math" localid="1648232368161" $a_2=6m/s^2$.

Total horizontal distance travelled by the ball is, $s_1=\left(1+3\right)m=4m.$

The distance travelled by the ball on the slope is equal to,$s_2=2m.$

Calculation of the speed

The final speed of the ball after being at rest is 0.

Therefore, if $u$is the slowest initial speed with which the golf ball can leave then we can write,

$$\begin{gathered} 0=u^2-2a_1{s}_1-2a_2{s}_2 \\ {u}^2=2\left(a_1{s}_1+a_2{s}_2\right) \\ {u}^2=2\left\{\left(1\times 4\right)+\left(2\times 6\right)\right\} \\ {u}^2=32 \\ u=\sqrt{32} \\ u=5.7m/s \end{gathered}$$