Kelvin is playing golf and tees off on a 190.0 m long par 3 hole. The ball leaves his club with a velocity of 50.0 m/s at 37.0o to the horizontal. 29.215
39.9
29.215? That's quite a specific number. Are you sure you didn't accidentally hit the "random decimal" button on your calculator? It happens to the best of us.
To find Kelvin's golf ball's horizontal range, we can decompose the initial velocity into its horizontal (x) and vertical (y) components.
Given:
Initial velocity (v₀) = 50.0 m/s
Launch angle (θ) = 37.0°
Step 1: Calculate the horizontal component of the initial velocity (v₀x).
v₀x = v₀ * cos(θ)
v₀x = 50.0 m/s * cos(37.0°)
v₀x = 50.0 m/s * 0.7986
v₀x = 39.93 m/s (rounded to two decimal places)
Step 2: Calculate the time of flight (t) for the ball.
The time of flight can be found using the vertical component of the initial velocity. The ball will follow a projectile motion trajectory, and the time taken to reach the maximum height is the same as the time taken to fall back to the ground.
To find the total time (t_total) of flight, use the formula:
t_total = 2 * (v₀y / g)
where g is the acceleration due to gravity (~9.8 m/s²) and v₀y is the vertical component of the initial velocity.
Given that the initial velocity (v₀) is at an angle of 37.0°, we need to find the vertical component (v₀y):
v₀y = v₀ * sin(θ)
v₀y = 50.0 m/s * sin(37.0°)
v₀y = 50.0 m/s * 0.6018
v₀y = 30.09 m/s (rounded to two decimal places)
Now, calculate the time of flight using t_total = 2 * (v₀y / g):
t_total = 2 * (30.09 m/s / 9.8 m/s²)
t_total = 2 * 3.0653 s
t_total = 6.13 s (rounded to two decimal places)
Step 3: Calculate the horizontal range (R) of the golf ball.
Given that Kelvin is playing on a flat surface (no elevation change), the horizontal range is given by:
R = v₀x * t_total
Calculate the horizontal range:
R = 39.93 m/s * 6.13 s
R = 244.45 m (rounded to two decimal places)
Therefore, Kelvin's golf ball will travel a horizontal distance of approximately 244.45 meters.