The projectile launch allows to find the results for questions about the movement are:
a) The initial velocity is: vo = 20 m/s with an angle of θ = 51.4º
b) The maximum height of the ball is: y = 12.5 m
c) The final velocity is: vo = 20 m/s with θ = 308.3º
The launch of projectiles is an application of kinematics where there is no acceleration on the x axis and the y axis is the gravity acceleration.
In the attachment we see a diagram of movement, the x-axis is horizontal and the y-axis is vertical.
They indicate that the range was x = 40 m and the ball was in the air t=3.2s.
a) Let's find the horizontal velocity, as there is no acceleration.
x = v₀ₓ t
v₀ₓ = x / t
let's calculate
v₀ₓ =
v₀ₓ = 12.5 m / s
We look for the vertical speed, when the ball reaches the destination its height is zero.
y = t - ½ g t²
0 = t - ½ g t²
0 = t ( - ½ g t)
The solution to this equation is:
t = 0 s Exit time.
- ½ g t = 0
= ½ g t
It indicates the time in the air that, because it is a scalar, is the same for the two movements.
Let's calculate
= ½ 9.8 3.2
= 15.68 m / s
We use the Pythagoras' theorem for the initial velocity modulus.
v₀ =
v₀ =
v₀ = 20 m / s
We use trigonometry for the angle.
tan θ =
θ = tam⁻¹
θ = tan⁻¹
θ = 51.4º
b) For the maximum height the vertical speed is zero.
0 =
y =
Let's calculate
y =
y = 12.5 m
C) The final velocity of the ball.
Since the x-axis there is no acceleration, the velocity is constant.
vₓ = 12.5 m / s
Let's find the final vertical speed.
= 15.68 - 9.8 3.2
= - 15.68 m / s
We are looking for the module.
v = vₓ² +
speed gives the same value.
v = 20 m / s
We use trigonometry for the angle.
θ'= tan⁻¹
θ' = -51.66º
This angle measured from the positive side of the x-axis counterclockwise is:
θ = 360 - θ'
θ = 360 - 51.66
θ = 308.3º
In conclusion, using the launch of projectiles we can find the results for questions about the movement are:
a) The initial velocity is: vo = 20 m / s with an angle of θ = 51.4º
b) The maximum height of the ball is: y = 12.5 m
c) The final velocity is: vo = 20 / s with θ= 308.3º
Learn more here: brainly.com/question/15063198