A ball is thrown upward at a speed v0 at an angle of 52.0˚ above the horizontal. It reaches a maximum height of 7.3 m. How high would this ball go if it were thrown straight upward at speed v0?
Well, let's see. If the ball reaches a maximum height of 7.3 m when thrown upwards at an angle of 52.0˚, and we want to know how high it would go if thrown straight upwards... I guess the answer is - well, it would go straight up, obviously! So, the height would be... wait for it... 7.3 meters! Ta-da!
To find out how high the ball would go if it were thrown straight upward at speed v0, we can break down the motion into its vertical and horizontal components.
Given:
Initial speed, v0
Angle above the horizontal, θ = 52.0˚
Maximum height reached, h = 7.3 m
First, let's find the vertical component of the ball's initial velocity, which we'll call v0y. This can be calculated using the formula:
v0y = v0 * sin(θ)
Next, we'll find the time it takes for the ball to reach its maximum height using the formula:
h = (v0y * t) - (0.5 * g * t^2)
Where g is the acceleration due to gravity (approximately 9.8 m/s^2) and t is the time taken to reach the maximum height.
Rearranging the above equation, we get:
h + (0.5 * g * t^2) = v0y * t
Since the ball is thrown straight upward, the final vertical velocity at its maximum height is 0. Therefore, we can solve the equation for t:
0 + (0.5 * g * t^2) = v0y * t
0.5 * g * t^2 = v0y * t
Simplifying further, we have:
0.5 * g * t = v0y
From this point, we can solve for t:
t = v0y / (0.5 * g)
Once we have the time, we can substitute it back into the original formula to find the height when the ball is thrown straight upward:
h = (v0y * t) - (0.5 * g * t^2)
Solve this equation to find the height.
A ball is thrown upward at a speed v0 at an angle of 56.0˚ above the horizontal. It reaches a maximum height of 6.9 m. How high would this ball go if it were thrown straight upward at speed v0?
The height is rises is proportional to (Vo*sinA)^2
Only the vertical component of velocity can be exchanged for gravitational potential energy.
Vo stays the same
The height ratio is therefore
H(90deg)/H(52deg) = (sin90/sin52)^2 = 1.610
H(90 deg) = 1.610*7.3 = 11.76 m