Question

A minigolf ball is on a perfectly horizontal surface, x = 2 m away from the center of the hole. There is a small obstacle in the way, so the ball cannot simply roll to the hole –it must go up in the air. The player is able to shoot with an initial speed v0 = 7 m/s. The ball can be launched at TWO possible angles with the horizontal for the ball to get in the hole. We want you to find these two angles.

Answer 1

Answer:

Two possible smallest and largest angles are 11.78° and 78.22°.

Step-by-step explanation:

Minigolf ball will follow a trajectory to get into the hole.

Since range of a trajectory is calculated by the formula,

$R=\frac{u^{2}sin2\theta}{g}$

Where u = initial speed of the ball

θ = angle between the hole and direction in which the ball has been projected

g = gravitational pull

Now we plug in the values in the formula,

$2=\frac{7^{2}sin(2\theta)}{9.8}$

sin2θ = $\frac{2\times 9.8}{49}$

2θ = $sin^{-1}(0.4)$

2θ = 23.57° or 156.43°

θ = 11.78° or 78.22°

Hence two possible smallest and largest angles are 11.78° and 78.22°.