Question

A golfer is teeing off on a 170.0m long par three hole. The ball leaves with a velocity of 40.0m/s at 50.0 degrees to the horizontal. Assuming that she hits the ball on a direct path to the hole, how far from the hole will the ball land (assuming no bounces or rolls)?

Answer 1

The golf ball will land approximately 74.11 meters from the hole.

Step-by-step explanation:

To determine how far from the hole the golf ball will land, we can analyze the horizontal and vertical components of its motion separately. The initial velocity of the ball is 40.0 m/s at an angle of 50.0 degrees to the horizontal. We can use trigonometry to find the horizontal component of the velocity, which is 40.0 m/s * cos(50.0 degrees) = 25.74 m/s. The time it takes for the ball to reach the ground can be found using the vertical component of its motion. The initial vertical velocity is 40.0 m/s * sin(50.0 degrees) = 30.47 m/s. Using the equation h = vo*t + 0.5*a*t^2, where h is the vertical displacement, vo is the initial velocity, a is the acceleration due to gravity (-9.8 m/s^2), and t is the time, we can solve for t. Plugging in the values, we have 0 = 30.47*t + 0.5*(-9.8)*t^2. This equation is a quadratic equation that can be solved using the quadratic formula. The positive root is the time it takes for the ball to reach the ground, which is approximately 2.88 seconds.

Now that we have the time, we can find the horizontal displacement of the ball using the horizontal component of its velocity and the time. The horizontal displacement is given by d = vo*t, which is 25.74 m/s * 2.88 seconds = 74.11 meters. Therefore, the golf ball will land approximately 74.11 meters from the hole.

Answer 2

d = 9.4 m

Step-by-step explanation:

As we know that the golfer hits the ball with speed 40 m/s at an angle of 50 degree

so here we will have range of the ball on the ground is given as

`R = (v^2 sin2\theta)/(g)`

so we will have

`R = (40^2 sin(2* 50))/(9.81)`

`R = 160.6 m`

So it will land at distance of 160.6 m

so the distance from the hole is given as

`d = 170 - 160.6`

`d = 9.4 m`