A football is kicked with an initial speed of 10.2 m/s at an angle of 40.00 above the horizontal. It lands on the ground 2.12 s later.

Determine the velocity of the football at the pinnacle of its trajectory.

7.66m/s

Explanation:

Horizontal component of initial speed is

= 10.2 × 0.7660

= 7.66 m/s

horizontal component of the final speed at pinnacle of its trajectory is

= 7.66 m/s

the vertical component of the speed at pinnacle of its trajectory is

the speed of the ball at pinnacle of the trajectory

=

= 7.66m/s

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west