Question

A golfer is going to hit a ball across horizontal ground at an initial angle of 24.4 degrees to the horizontal. If he wants the ball to travel a distance of 176 m before it hits the ground, what should the initial speed of the ball be, in units of m/s?

Answer 1

To calculate the initial speed of a golf ball that must travel 176 meters at a launch angle of 24.4 degrees, we apply the projectile motion formula v = sqrt((R * g) / sin(2 * theta)), using the given range and angle, and solve for v.

Step-by-step explanation:

To find the initial speed of a golf ball that needs to travel 176 meters at an initial angle of 24.4 degrees, we can use the projectile motion equations from physics. Assuming no air resistance, the horizontal distance (range) the ball travels can be determined by the following equation:

R = (v^2 * sin(2*theta)) / g

Where:

• R is the range,
• v is the initial velocity,
• theta is the launch angle,
• g is the acceleration due to gravity (9.81 m/s2).

Rearranging the equation to solve for the initial velocity (v), we get:

v = sqrt((R * g) / sin(2 * theta))

Plugging in our known values (R = 176 m, theta = 24.4 degrees):

v = sqrt((176 m * 9.81 m/s2) / sin(2 * 24.4 degrees))

Calculating this result gives us the initial speed required to achieve the desired range.