Question

What is the correct crosswind equation to find the height of an object at 10 meters?

1) h = (v² * sin²(θ)) / (2 * g)
2) h = (v² * cos²(θ)) / (2 * g)
3) h = (v² * sin(θ)) / (2 * g)
4) h = (v² * cos(θ)) / (2 * g)

Answer 1

The correct equation to find the maximum height h of a projectile with initial velocity v and launch angle θ is: h = (v² * sin²(θ)) / (2 * g), which uses the sine function to consider the vertical component of the velocity.

Step-by-step explanation:

The correct crosswind equation to find the height of an object at 10 meters, assuming the object is a projectile being launched at an angle θ from the ground with an initial velocity v, is the one that uses the vertical component of the velocity. We consider the projectile motion equations, where h represents the maximum height reached by the object, v is the initial velocity, and θ is the launch angle.

The correct equation from the options provided is:

h = (v² * sin²(θ)) / (2 * g)

This is because the sine function represents the vertical component of the velocity when considering the angle of launch, and we are interested in how high the object goes. To find the height h, we use the following kinematic equation for projectile motion which considers gravity g as the acceleration acting on the object:

h = (v² * sin²(θ)) / (2 * g)

This equation represents the maximum height a projectile can reach based on its initial velocity and the angle of launch, with gravity being the only force acting on the projectile after it is launched.