A tennis ball is thrown with a velocity of 30m/s at an angle of 60^ of the horizontal calculate the time,m/s,and the range
U = hor speed = 30 cos 60 = 15
Vi - initial ver speed = 30 sin 60
= 26
get time upward
v + Vi - 9.81 t
0 = 26 - 9.81 t at top
t = 26/9.81 that is half total time
range = 2 * 15 * 26/9.81
To calculate the time, velocity, and range of a tennis ball thrown at an angle, we can use the equations of projectile motion.
1. Time (t):
The time of flight can be calculated using the equation: t = 2 * (v * sinθ) / g
where v is the initial velocity and θ is the launch angle, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Given:
v = 30 m/s
θ = 60 degrees
Converting the launch angle to radians:
θ (in radians) = θ (in degrees) * π / 180
θ (in radians) = 60 * π / 180
θ (in radians) = π / 3
Now substitute the values into the equation:
t = 2 * (30 * sin(π / 3)) / 9.8
Evaluating the expression:
t = 2 * (30 * 0.866) / 9.8
t = 52.2 / 9.8
t ≈ 5.33 seconds (rounded to two decimal places)
So, the time of flight of the tennis ball is approximately 5.33 seconds.
2. Vertical velocity (m/s):
The vertical velocity of the tennis ball at any given time can be calculated using the equation: vy = v * sinθ
Given:
v = 30 m/s
θ = 60 degrees
Substituting the values into the equation:
vy = 30 * sin(60)
Evaluating the expression:
vy = 30 * 0.866
vy ≈ 25.98 m/s (rounded to two decimal places)
So, the vertical velocity of the tennis ball is approximately 25.98 m/s.
3. Range (m):
The horizontal distance covered by the tennis ball can be calculated using the equation: R = v * cosθ * t
Given:
v = 30 m/s
θ = 60 degrees
t = 5.33 seconds (as calculated earlier)
Substituting the values into the equation:
R = 30 * cos(60) * 5.33
Evaluating the expression:
R = 30 * 0.5 * 5.33
R ≈ 79.95 meters (rounded to two decimal places)
So, the range of the tennis ball is approximately 79.95 meters.