Astudent throws a water balloon with speed v0 from a height h = 1.82 m at an angle θ = 29° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 7.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. determine the magnitude of the balloon's initial velocity, v0, in meters per second.

The magnitude of the balloon's initial velocity is 7.80 m/s

The given parameter

To find:

The vertical component of the velocity is calculated as;

The horizontal component of the velocity is given as;

The horizontal distance or range of the projectile is given as;

The change in vertical height of the balloon is given as;

assume the balloon falls to zero position

The magnitude of initial velocity of the balloon is calculated as;

Thus, the magnitude of the balloon's initial velocity is 7.80 m/s

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Explanation:

As we projected the balloon at speed vo at an angle of 29 degree

so the two component of velocity is given as

now we know that in x direction we have

in y direction we have

now we have