A golf ball is hit with an initial velocity of 135 feet per second at an angle of 22 degree above the horizontal. will the ball clear a 25-foot-wide sand trap whose nearest edge is 300 feet from the golfer?
To determine if the golf ball will clear the sand trap, we need to calculate its horizontal and vertical distances.
First, let's calculate the horizontal distance the ball will travel. We can use the initial velocity and angle of launch to find the horizontal component of the velocity.
Horizontal component of velocity = initial velocity * cos(angle)
Given:
Initial velocity = 135 feet per second
Angle = 22 degrees
Using these values, we can calculate the horizontal component of velocity as follows:
Horizontal component of velocity = 135 ft/s * cos(22 degrees)
Next, we need to find the time it takes for the ball to reach the sand trap, which is 300 feet away from the golfer. The time can be calculated using the horizontal distance divided by the horizontal component of velocity:
Time = Horizontal distance / Horizontal component of velocity
Given:
Horizontal distance = 300 feet
Horizontal component of velocity = 135 ft/s * cos(22 degrees)
Using these values, we can calculate the time as follows:
Time = 300 ft / (135 ft/s * cos(22 degrees))
Once we have the time, we can find the vertical distance the ball will travel using the following kinematic equation:
Vertical distance = Initial velocity * sin(angle) * time - (1/2) * gravity * time^2
Given:
Initial velocity = 135 feet per second
Angle = 22 degrees
Time (calculated in the previous step)
Using these values and assuming gravity is approximately 32 feet per second squared, we can calculate the vertical distance traveled by the ball:
Vertical distance = 135 ft/s * sin(22 degrees) * time - (1/2) * 32 ft/s^2 * time^2
Now, let's compare the vertical distance to the height of the sand trap, which is 25 feet. If the vertical distance is greater than 25 feet, the ball will clear the sand trap. Otherwise, it will not.
So, calculate the vertical distance using the formula mentioned above and compare it to 25 feet to determine whether the ball will clear the sand trap.