I just started the preview course, and I need help to find out the answer. Explain to me. And if it's possible for yall to show me diagrams or videos, thanks. What equations do I use and how do I go about doing things?
A golfer hits a golf ball at an angle of 25.0(degrees) relative to the ground. If the golf ball covers a horizontal distance of 301.5m, what is the ball's maximum height? (Hint: At the top of its flight, the ball's vertical velocity component will be zero.)
electron12015-06-30T14:40:39Z
During the time that the ball is in the air, its vertical velocity decreases at the rate of 9.8 m/s each second. The horizontal velocity is constant. The first step is to determine the vertical and horizontal components of the ball’s initial velocity.
Vertical = v * sin 25, Horizontal = v * cos 25 Let’s use the following equation to determine the time.
d = v * t, d = 301.5 meters, v = v * cos 25 301.5 = v * cos 25 * t t = 301.5 ÷ (v * cos 25)
Since the ball’s vertical velocity is 0 m/s when it reaches the maximum height, let’s use the following equation to determine the time.
vf = vi – a * t, vf = 0, vi = v * sin 25, a = 9.8 0 = v * sin 25 – 9.8 * t t = v * sin 25 ÷ 9.8 Let’s set these two equations equal to each other.
301.5 ÷ (v * cos 25) = v * sin 25 ÷ 9.8 Multiply both sides by 9.8. 2954.7 ÷ (v * cos 25) = v * sin 25 Multiply both sides by v * cos 25. 2954.7 = v^2 * cos 25 * sin 25 2 * sin 25 * cos 25 = sin 50
cos 25 * sin 25 = sin 50/2 2954.7 = v^2 * sin 50/2 5909.4 = v^2 * sin 50 v^2 = 5909.4 ÷ sin 50 v = √(5909.4 ÷ sin 50) = 87.83036967 m/s
To check this answer, let’s determine the vertical and horizontal components of the ball’s initial velocity.
Vertical = 87.83036967 * sin 25, Horizontal = 87.83036967 * cos 25 Let’s determine the time.
t = 301.5 ÷ (87.83036967 * cos 25) = 3.78624302 seconds t = 87.83036967 * sin 25 ÷ 9.8 = 3.787624302 seconds This proves that the initial velocity is correct.
U would not be previewing a question like this *early* unless you had some background in physics because it is not elementary but takes several steps to derive the solution equation plus knowledge of elementary motion. Go to the source page under "Range of Trajectory" for more: R = Vo²(sin 2Θ/g) 301.5 = Vo²(0.7660/9.81) = 0.07809Vo² Vo² = 3861.0 62.1 m/s ANS