A golfer hits a golf ball with a velocity of 36.0 meters/second at an angle of 28.0°. If the hang time of the golf ball is 3.44 seconds, what is the range of the golf ball?
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t= 2vₒ•sinα/g
L=vₒ²•sin2α/g,
To find the range of the golf ball, we need to calculate the horizontal distance it covers during its hang time.
Step 1: Calculate the horizontal component of the initial velocity:
The horizontal component of the initial velocity is given by: Vx = V * cos(θ), where V is the magnitude of the velocity and θ is the launch angle.
Vx = 36.0 m/s * cos(28.0°)
Vx = 36.0 m/s * 0.882
Vx = 31.752 m/s
Step 2: Calculate the horizontal distance:
To find the horizontal distance covered during hang time, we use the equation: d = Vx * t, where Vx is the horizontal component of the velocity and t is the hang time.
d = 31.752 m/s * 3.44 s
d = 109.180288 m
Therefore, the range of the golf ball is approximately 109.18 meters.
To find the range of the golf ball, we need to determine the horizontal distance it travels.
The horizontal velocity of the golf ball can be calculated using the equation:
Vx = V * cos(θ)
where Vx is the horizontal velocity, V is the initial velocity of the golf ball, and θ is the launch angle.
Plugging in the values given in the problem:
V = 36.0 meters/second
θ = 28.0°
Vx = 36.0 * cos(28.0°)
Next, we'll calculate the hang time of the golf ball. The hang time is the time the ball remains in the air. Since the initial vertical velocity is zero, we can use the equation:
t = 2 * Vy / g
where t is the hang time, Vy is the vertical velocity, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Since the ball will travel upward for half the hang time and downward for the other half, we can calculate the vertical velocity:
Vy = g * t / 2
Plugging in the values given in the problem:
t = 3.44 seconds
g = 9.8 m/s^2
Vy = 9.8 * 3.44 / 2
Now that we have the horizontal and vertical velocities, we can calculate the range using the equation:
Range = Vx * t
Plugging in the values we have determined:
Range = (36.0 * cos(28.0°)) * 3.44
Evaluating this expression will give us the range of the golf ball.
Note: Make sure to convert the angle from degrees to radians if the trigonometric functions in your calculator require it.