Question

given numeric values for the variables in the problem statement, θ=34.2∘ , h=1.51m , and d=7.39m , determine the magnitude, in meters per second, of the balloon's initial velocity.

Answer 1

To determine the magnitude of the balloon's initial velocity, use the concepts of projectile motion, calculate the time it takes for the balloon to fall to the ground, find the initial horizontal velocity, and then calculate the magnitude of the initial velocity using the horizontal and vertical velocities.

Step-by-step explanation:

To determine the magnitude of the balloon's initial velocity, we can use the concept of projectile motion. Since the balloon is launched horizontally, the initial horizontal velocity (Vx) is equal to the initial velocity of the balloon. The vertical velocity (Vy) is affected by gravity, so we can use the equation Vy = gt, where g is the acceleration due to gravity (9.8 m/s^2). Using the given variables θ=34.2∘ , h=1.51m, and d=7.39m, we can calculate the initial velocity using the equation v = √(Vx^2 + Vy^2).

First, let's find the time it takes for the balloon to fall to the ground, t. We can use the equation h = 0.5gt^2, rearrange it to t = √(2h/g), and substitute the given values to find t. Substituting the value of t into the equation d = Vx * t, we can solve for Vx. Finally, using Vx and Vy, we can calculate the magnitude of the initial velocity v = √(Vx^2 + Vy^2).

By substituting the given values into the equations, we find that the magnitude of the balloon's initial velocity is approximately 4.16 m/s.