A stone is projected upward at an angle of 60degree to the horizontal from the top of a tower of height 100meter and it hits the ground at a point. If the initial velocity of projection is 100meter. Calculate the maximum height of the stone above the ground. Calculate the time it takes to reach this height. Calculate the time of flight
100 m/s I assume you mean
thus vi = initial speed up = 100 sin 60
v = vi - 9.8 t
at top v = 0
so at top
9.8 t = 100 sin 60
solve for t, time to top
total time is twice that by symmetry
h = vi t - 4.9 t^2
What is time of flight
To calculate the maximum height attained by the stone, we can use the equations of projectile motion.
Let's break down the initial velocity of the stone into its horizontal and vertical components. The horizontal component remains constant throughout the motion, while the vertical component is affected by gravity.
Given:
Initial velocity, u = 100 m/s
Angle of projection, θ = 60 degrees
Height of the tower, h = 100 meters
Step 1: Calculate the initial vertical velocity (Vy) component:
Vy = u * sin(θ)
= 100 * sin(60)
≈ 86.6 m/s (rounded to one decimal place)
Step 2: Calculate the time taken to reach the maximum height (t_max):
At the maximum height, the vertical velocity becomes zero, as the stone momentarily comes to rest before falling back down. Use the equation:
Vy = u_y + g * t
Where g is the acceleration due to gravity (approximately 9.8 m/s^2).
0 = Vy - g * t_max
-86.6 = -9.8 * t_max
t_max ≈ 8.8 s (rounded to one decimal place)
Step 3: Calculate the maximum height (H_max) using the time calculated above:
H_max = u_y * t_max - 0.5 * g * t_max^2
= 86.6 * 8.8 - 0.5 * 9.8 * (8.8)^2
≈ 380.6 m (rounded to one decimal place)
So, the maximum height attained by the stone is approximately 380.6 meters.
Now let's calculate the total time of flight (t_flight), which is the time taken for the stone to hit the ground after being projected upwards.
t_flight = 2 * t_max
≈ 2 * 8.8
≈ 17.6 s (rounded to one decimal place)
Therefore, the time of flight for the stone is approximately 17.6 seconds.