Physics Hw

Question

Chapter 03, Problem 03 GO


In a football game a kicker attempts a field goal. The ball remains in contact with the kicker's foot for 0.0634 s, during which time it experiences an acceleration of 150 m/s2. The ball is launched at an angle of 53.0° above the ground. Determine the (a) horizontal and (b) vertical components of the launch velocity.


(a) Number

Units




(b) Number

Units

Answer 1

Hi Rae!

 

On this problem, we need to determine the final velocity of the ball after it is accelerated by the kicker's foot.  We can then decompose that final velocity into its components, based on the given angle.

 

If we treat the kicker's acceleration of the football as constant (implied by the problem), we can use kinematics to find the final velocity, since the motion is then implied to take place all along one line (starting from rest).  We treat this one line as our one dimension, even though it is slanted with respect to x and y.  The final velocity we compute will be along this line; then we can solve for its horizontal and vertical components in the last step.

 

First, I list the kinematic quantity we are trying to calculate:

 

to find:  v  (final velocity)

 

And we have to know three other kinematic quantities for this motion.

 

know: a (= 150 m/s², given, which we can take to be in the positive direction along our line), v_o (= 0 m/s, since the ball starts at rest), and t (=0.0634 s, given)

 

Knowing these four quantities, we can use the kinematic equation relating them all:

 

v = v_o + at

v = 0 m/s + (150 m/s²)(0.0634 s) = 9.51 m/s  

 

This is the overall final velocity of the football along the (slanted) line of its launch.  Then we can get the horizontal and vertical components by:

 

v_x = vcosθ = (9.51 m/s)cos(53^o) = 5.72 m/s

v_y = vsinθ = (9.51 m/s)sin(53^o) = 7.60 m/s

 

I hope this helps!  As always, I will check my math again, and if you have any questions or concerns with any of this, just let me know.