A batted baseball, which leaves the bat at an angle 〖30〗^0 above the horizontal, is caught by an outfielder 120m from the plate.
a.) What is the initiated velocity of the ball?
b.) How high did it rise?
c.) How long was it in the air?
my friend asked that question. I really want to help her but i do not know where to start. I am not good in physics.
.please help me to answer this question. Thanks :)
a) The distance the ball travels is
D = Vo^2*sin60/g = 120 m
Solve for the initial velocity Vo
Vo^2 = 120*9.8/sin60 = 1358 m^2/s^2
Vo = 36.85 m/s
b) H = Vo^2sin^2(30)/(2*g)
c) Hang time = 2*Vo*sin30/g
Sure, I'd be happy to help you with this physics problem! Let's break it down step by step.
a.) To find the initial velocity of the ball, we can use the following equation of motion:
v₀x = v₀ * cos(θ)
where v₀x is the initial velocity in the horizontal direction, v₀ is the initial velocity of the ball, and θ is the angle at which the ball leaves the bat (30° above the horizontal).
Since we're given the distance the ball travels horizontally (120m), we can use this information to solve for v₀x:
v₀x = (distance) / (time)
To find the time, we need to know how long the ball was in the air for, which we'll calculate in part c.
b.) To find the height the ball rises, we can use the equation:
Δy = (v₀sin(θ))^2 / (2g)
where Δy is the change in height, v₀ is the initial velocity of the ball, θ is the angle at which the ball leaves the bat (30° above the horizontal), and g is the acceleration due to gravity (approximately 9.8 m/s²).
c.) To find the time the ball was in the air, we'll use the following equation of motion:
Δy = v₀y * t - (1/2)g * t²
where Δy is the change in height (which we calculated in part b), v₀y is the initial vertical velocity of the ball, g is the acceleration due to gravity, and t is the time the ball was in the air.
To calculate v₀y, we can use the initial velocity v₀ and the angle θ:
v₀y = v₀ * sin(θ)
By rearranging the equation, we can solve for t:
t = (v₀y + √(v₀y² + 2gΔy)) / g
Now that we have all the necessary equations, let's calculate the answers!
1. Calculate v₀x:
v₀x = (distance) / (time)
2. Calculate Δy:
Δy = (v₀sin(θ))^2 / (2g)
3. Calculate t:
t = (v₀y + √(v₀y² + 2gΔy)) / g
I hope this helps you to solve the problem! Let me know if you have any further questions.