What is the total time of flight of an object projected vertically upwards with a speed of 30m/s? (g=10m/s^2
I need an answer
To find the total time of flight of an object projected vertically upwards, we can use the equation of motion:
Δy = v₀t + (1/2)gt²
Where:
Δy is the displacement (change in height),
v₀ is the initial velocity,
t is the time of flight,
g is the acceleration due to gravity.
In this case, the object is projected vertically upwards, so the initial velocity (v₀) is 30 m/s and the acceleration due to gravity (g) is -10 m/s² (negative because it opposes the motion).
Since the object is moving upward, the final displacement (Δy) is zero because it eventually reaches its peak and comes back down to the starting point.
So, we can rewrite the equation as:
0 = 30t - (1/2)(10)t²
Simplifying the equation, we have:
-5t² + 30t = 0
Factorizing the equation, we get:
t(-5t + 30) = 0
From this equation, we have two possible solutions:
1) t = 0 (Initial time, when the object is at ground level).
2) -5t + 30 = 0
Solving the second equation for t, we have:
-5t = -30
t = -30 / -5
t = 6 seconds
Since we are only interested in the positive time, the total time of flight is 6 seconds.
time up equals time down
flight time = 2 * 30 m/s / 10 m/s²