physics projectile motion question please help

Question

Thelma and Louise drive their '66 T-Bird convertible off a cliff. They are going 24.1 m/s and the cliff is 44 meters high. Find the magnitude of their velocity vector the moment they impact the ground. Make sure you do the following in your answer:
DO NOT include units. We'll deal with that in the next question.
Give precision to tenths (#.#).
Make your answer correct to within 0.2

Answer 1

Hi Lauren.

 

Horizontal components of velocity do not change when you decide to neglect air drag (which in this case we do). It will be 24.1 m/sec throughout the fall.

 

To find the vertical component, there are several methods you can employ. The easiest is using conservation of energy. The potential energy at the top of the cliff will equal the kinetic energy at the bottom of the cliff.

 

mgh = 1/2mv²

 

gh = 1/2v²

 

(9.8)(44) = 1/2*v²

 

v = 29.37 m/sec

 

Another method is to determine how long the fall took, then multiplying that by the acceleration due to gravity.

 

h = 1/2gt²

 

44 = 1/2*9.8*t²

 

t = 2.997 sec

 

v = gt = 9.8*2.997 = 29.37 m/sec

 

So, the vertical component is 29.37 m/sec. The horizontal component is 24.1 m/sec. Therefore, the overall magnitude is:

 

√(29.37² + 24.1²) = 37.99 m/sec

 

Hope this helps.