a ball rolls off an incline at an angle of 30 below the horizontal at a velocity of 22m/s. how far from the base will the ball hit the floor if it lands in 3s?
Its horizontal velocity= 22cos30
distance=horizVelocity*time
To find how far the ball will hit the floor, we need to determine the horizontal distance it travels.
Given:
Angle below the horizontal (θ) = 30°
Initial velocity (v₀) = 22 m/s
Time of flight (t) = 3 s
First, let's find the horizontal component of the initial velocity (v₀x) using the trigonometric relationship:
v₀x = v₀ * cos(θ)
Plugging in the values:
v₀x = 22 * cos(30°)
Calculating:
v₀x ≈ 19.03 m/s (rounded to two decimal places)
Now that we have the horizontal component of the initial velocity, we can calculate the horizontal distance the ball travels:
d = v₀x * t
Plugging in the values:
d = 19.03 * 3
Calculating:
d ≈ 57.09 m (rounded to two decimal places)
Therefore, the ball will hit the floor approximately 57.09 meters from the base.