Aball of mass m is thrown into the air in a 45° direction of the horizon, after 3 seconds the ball is seen in a direction 30° from the horizon. ignoring the friction of the air, find the initial velocity v of the ball.

Velocity (magnitude) is 98.37 m/s

Explanation:

We use the vertical component of the initial velocity, which is:

Using kinematics expression of vertical velocity (in y direction) for an accelerated motion (constant acceleration, which is gravity):

Now we need to find as a function of . We use the horizontal velocity, which is always the same as follow:

We know the angle at 3 seconds:

Substitute   in   and then solve for  

With this expression we go back to the kinematic equation and solve it for initial speed

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0 = 0.40 / 0 = 0

= 0.20 = 9.80 ⁄2 =?

=0 , = = 0.20 =0.50 0 0.40 ⁄

=0−122 =0−12(9.80 ⁄2)(0.50)2 =1.2