Afootball player punts the ball at a 45.0º angle. when the ball returns to the ground, it will have a horizontal displacement of 60.6 m. what is the initial speed of the ball?

Step-by-step explanation:

Consider the vertical motion of ball,  

   We have equation of motion v = u + at  

   Initial velocity, u = u sin θ  

   Final velocity, v = -u sin θ  

   Acceleration = -g  

Substituting  

   v = u + at  

   -u sin θ = u sin θ - g t  

This is the time of flight.  

Consider the vertical motion of ball till maximum height,  

  We have equation of motion v² = u² + 2as  

  Initial velocity, u = u sin θ

  Acceleration, a = -g  

  Final velocity, v = 0 m/s  

Substituting  

  v² = u² + 2as  

  0² = u²sin² θ + 2 x -g x H

This is the maximum height reached,  

Consider the horizontal motion of ball,  

  Initial velocity, u = u cos θ  

  Acceleration, a =0 m/s²  

  Time,  

Substituting  

  s = ut + 0.5 at²  

This is the range.  

Here θ = 45° and S = 60.6 m

Substituting

Initial speed of the ball is 24.38 m/s

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step-by-step explanati∵∵∴∴on:

15

step-by-step explanation:

we are given the following expression and we are to solve it and find the product:

-13 × (-5)

solving the given expression in the standard order of solving a mathematical expression, beginning with the opening of brackets and then multiplying the terms and changing their signs.

-3 × -5 = 15 (answer is positive because when negative is multiplied with negative, it gives a positive answer)