Find Initial Velocity & Angle of Projection for a Projectile at 40m

[sanjaymodi]

Homework Statement

If at height of 40 m the direction of motion of a projectile makes an angle 45 degrees with
the horizontal, then what is its initial velocity and angle of projection?

Homework Equations

The Attempt at a Solution

 

[anastasiao]

I don't really know how much help i can be but from what i remember you the x and y times will be the same. So 40m and the acceleration of gravity with the angles are what you need to solve the problem

 

[ogb p]

To find the initial velocity and angle of projection for a projectile at 40m, we can use the following equations:

1. Vertical displacement equation: h = ut*sin(theta)*t - 0.5*g*t^2, where h is the height, u is the initial velocity, theta is the angle of projection, t is time, and g is the acceleration due to gravity.

2. Horizontal displacement equation: x = u*cos(theta)*t, where x is the horizontal distance, u is the initial velocity, and theta is the angle of projection.

Using these equations, we can solve for u and theta by setting the initial height (h) to 40m and the angle (theta) to 45 degrees. We also know that the initial horizontal velocity (u*cos(theta)) is equal to the initial vertical velocity (u*sin(theta)) since the angle is 45 degrees.

Substituting these values into the equations, we get:

40 = u*sin(45)*t - 0.5*g*t^2

x = u*cos(45)*t

Solving for t in the first equation and substituting it into the second equation, we get:

x = u*cos(45)*(40/u*sin(45)) - 0.5*g*(40/u*sin(45))^2

x = 40*tan(45) - 0.5*g*(40/tan(45))^2

x = 40 - 0.5*g*1600/tan(45)^2

x = 40 - 0.5*g*1600/1

x = 40 - 800g

Solving for u, we get:

u = x/(cos(45)*t)

Substituting in the value of x from the equation above, we get:

u = (40 - 800g)/(cos(45)*t)

Substituting in the value of t from the first equation, we get:

u = (40 - 800g)/(cos(45)*(40/u*sin(45)))

Solving for u, we get:

u = 40/tan(45) - 800g/tan(45)

u = 40 - 800g

Therefore, the initial velocity of the projectile is 40 - 800g m/s and the angle of projection is 45 degrees. This means that the projectile was launched at a speed of 40 - 800