Pablo kicks a football with an initial velocity of 30 feet per second at an angle of 58° with the horizontal. After 0.3 seconds, how far does the ball travel vertically? Round to the nearest hundredth
To find out how far the ball has traveled vertically after 0.3 seconds, we need to calculate the vertical displacement or the change in vertical position.
The vertical motion of the ball can be analyzed independently of its horizontal motion because they are separate components. The key parameter we need to consider is the initial vertical velocity (Vy).
Given:
Initial velocity (V) = 30 feet per second
Launch angle (θ) = 58°
To find the initial vertical velocity, we use the formula:
Vy = V * sin(θ)
Plugging in the given values:
Vy = 30 * sin(58°)
Calculating this value:
Vy ≈ 25.84 feet per second (rounded to the nearest hundredth)
Now, we can find the vertical displacement (Δy) using the following formula:
Δy = Vy * t + (1/2) * g * t^2
Where:
t = time = 0.3 seconds
g = acceleration due to gravity ≈ 32.2 feet per second squared
Plugging in the values:
Δy = (25.84 * 0.3) + (0.5 * 32.2 * 0.3^2)
Calculating this value:
Δy ≈ 3.87 feet (rounded to the nearest hundredth)
Therefore, after 0.3 seconds, the ball has traveled approximately 3.87 feet vertically.