Vo = 25m/s @ 35o
Xo = 25*cos35 = 20.48 m/s.
Dx = Xo*t = 38 m.
t = 38/Xo = 38/20.48 = 1.86 s.
Xo = 25*cos35 = 20.48 m/s.
Dx = Xo*t = 38 m.
t = 38/Xo = 38/20.48 = 1.86 s.
First, let's resolve the initial velocity of the football into its horizontal and vertical components:
Horizontal component: Vx = V * cos(θ)
Vertical component: Vy = V * sin(θ)
Given:
- Angle of 35 degrees: θ = 35 degrees
- Speed of 25 m/s: V = 25 m/s
Using these values, we can calculate the horizontal and vertical components of velocity:
Vx = 25 m/s * cos(35 degrees)
Vy = 25 m/s * sin(35 degrees)
Next, we need to find the time it takes for the football to reach a horizontal distance of 38m. The horizontal distance traveled by an object can be calculated using the formula:
Distance = Velocity * Time
Since the football's initial horizontal velocity is constant (there is no horizontal acceleration), we can solve for time using the formula:
Time = Distance / Velocity
Plugging in the given values:
Time = 38 m / Vx
Now we can calculate the time the football was in the air:
Time = 38 m / (25 m/s * cos(35 degrees))
Calculating the value using a calculator:
Time ≈ 38 m / (25 m/s * 0.819)
So, the football was in the air for approximately:
Time ≈ 1.84 seconds