a golf ball is struck at a 45 degree angle and flies off at 28m/s. what is the range? using the SOH CAH TOH method and the range formula.
The range (on the fly) is V^2/2g = 40 m when hit at that 45 degree angle. The golf ball will in most cases roll farther than that.
I am not familiar with the SOH CAH TOH method.
sin of angle = opp/hyp (SOH)
cos of angle = adj/hyp (CAH)
tan of angle = opp/adj (TOA)
To find the range of the golf ball, we can use two methods: the SOH CAH TOH method and the range formula.
1. Using the SOH CAH TOH method:
- In this method, we will use the sine function (SOH) to determine the vertical displacement (height) of the golf ball.
- The angle of 45 degrees suggests that we are looking for the height of the golf ball at the highest point of its trajectory.
- Sin(45) = opposite/hypotenuse
- Hypotenuse is the initial velocity of the ball, which is 28 m/s. Since we are finding the vertical displacement, the opposite side will represent the height.
- So, sin(45) = height/28
- Solving for the height, height = 28 * sin(45)
- Calculating the result, height ≈ 19.8 m
2. Using the range formula:
- The range formula is given by: range = (v^2 * sin(2θ)) / g
- Where v is the initial velocity of the ball, θ is the angle, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
- Substituting the given values, the range = (28^2 * sin(2 * 45)) / 9.8
- Simplifying further, the range ≈ (784 * sin(90)) / 9.8
- Since sin(90) = 1, the range ≈ 784 / 9.8
- Calculating the result, the range ≈ 80 m.
Using either method, we find that the range of the golf ball is approximately 80 meters.