4. 2D Kinematics

A football at rest is kicked by a football kicker. The ball is in contact with the kicker's foot for 0.050s, during which it experiences an acceleration a = 340 m/s². The ball is launched at an angle of 40° above the ground (x-axis). Calculate the horizontal and vertical components of the launch velocity.

A car is moving with speed 16.0 m/s due south at one moment and 25.7 m/s due east 8.00 s later. Over this time interval, determine the magnitude and direction of (a) its average velocity, (b) its average acceleration. (c) What is its average speed? [Hint: Can you determine all these from the information given?]

A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by $\vec{v} = \left[ 5.00~\mathrm{m/s} - (0.0180~\mathrm{m/s^3})t^2 \right] \hat{i} + \left[ 2.00~\mathrm{m/s} + (0.550~\mathrm{m/s^2})t \right] \hat{j}$. What are the magnitude and direction of the car's velocity at $t=8.00s$? (b) What are the magnitude and direction of the car's acceleration at $t=8.00s$?

The coordinates of a bird flying in the xy-plane are given by x(t) = αt and y(t) = 3.0 m − βt², where α = 2.4 m/s and β = 1.2 m/s². Calculate the magnitude and direction of the bird's velocity and acceleration at t = 2.0 s.

Complete the motion diagram by adding acceleration vectors.