A stone is thrown from the top of a building upward at an angle of 30.0 to the horizontal and with an initial speed of 25.0m/s ,if the heights of the building is 75.0m..How long is the flight?
hf=hi+vi*t-4.9t^2
0=75+25*t-4.9t^2
solve this quadratic equaation with the qudratic formula....
To find the total time of flight, we can break down the motion into horizontal and vertical components.
Given:
Initial speed, v₀ = 25.0 m/s
Angle of projection, θ = 30.0°
Height of the building, h = 75.0 m
First, let's find the time taken to reach the maximum height.
Vertical component:
The initial vertical velocity (v₀sinθ) is given by:
v₀sinθ = 25.0 m/s * sin(30.0°) = 12.5 m/s
We can use the kinematic equation:
v = u + at,
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.
At the highest point, the final velocity is 0 m/s, so we have:
0 = 12.5 m/s - 9.8 m/s² * t_max_height
t_max_height = 12.5 m/s / (9.8 m/s²)
t_max_height ≈ 1.276 s
Next, let's find the total time of flight.
Since the stone takes the same amount of time to rise to the maximum height and fall back down, the total time of flight is twice the time taken to reach the maximum height.
Total time of flight = 2 * t_max_height
Total time of flight ≈ 2 * 1.276 s
Total time of flight ≈ 2.552 s
Therefore, the total time of flight is approximately 2.552 seconds.
To find the duration of flight of the stone, we need to calculate the time it takes for the stone to reach its highest point and then double that time, as the stone will take the same amount of time to descend back to the ground.
First, we need to find the vertical component of the initial velocity. We can use the formula:
v_y = v * sin(θ)
Where v is the initial velocity (25.0 m/s) and θ is the launch angle (30°).
v_y = 25.0 m/s * sin(30°)
v_y = 25.0 m/s * 0.5
v_y = 12.5 m/s
Now we can use the vertical motion equation:
h = v_y * t - 0.5 * g * t^2
Where h is the height (75.0 m), v_y is the vertical component of the initial velocity (12.5 m/s), g is the acceleration due to gravity (9.8 m/s^2), and t is the time in seconds.
Since the stone reaches its highest point when its vertical velocity becomes zero, we can set v_y = 0 and solve for t:
0 = 12.5 m/s - 9.8 m/s^2 * t
9.8 m/s^2 * t = 12.5 m/s
t = 12.5 m/s / 9.8 m/s^2
t ≈ 1.28 s
Doubling this time gives us the total duration of the flight:
Total time = 2 * t
Total time = 2 * 1.28 s
Total time ≈ 2.56 s
Therefore, the duration of the flight is approximately 2.56 seconds.