# modelling projectile motion problem

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A football is kicked across a level field. The ball spends 3 seconds in the air and lands 60 m from the point where it was kicked. (Ignore air resistance).

a) What is the speed of the ball at the top of its trajectory in m per second

b) What is the maximum height H reached by the ball in m?

c) What is the y-component of the initial velocity that the football is kicked at? 5.3 m per second?

d) What is the speed at which the football lands on the ground in m per second?

e) What is the angle (measured relative to horizontal) that the football hits the ground at in degrees?

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A projectile motion problem is described as modelling problem in the solution.

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When a football is kicked in a direction, say at an angle theta with the horizontal, it experiences gravitational force (m*g) in vertical downward direction. As air resistance is neglected, only the gravitational force influences it's trajectory. In horizontal direction no force acting on the particle, hence in horizontal direction the football will have uniform motion. Under gravitational force, velocity of the football will change in vertical direction with time.

Hence, this problem can be considered as two dimensional motion (horizontal and vertical). In horizontal direction, no acceleration/zero acceleration. In vertical direction there will be non-zero constant acceleration in vertical down-ward direction.

In vertical direction,

F = m*g = m*a

=> a = g (vertically downward)

In horizontal direction,

F = 0: acceleration = 0.

Initial velocity can be resolved in horizontal as well as in vertical direction,

u_h = ...

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