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Projectile Motion

Scott kicked a football with an initial velocity of 50 ft/sec at an angle of 65 degrees with the horizontal and at a height of 3 feet. Write the equations that would model this situation and answer the following:

a)
x(t) = _____________ (fill in formula with variable values plugged in)
y(t) = _____________ (fill in formula with variable values plugged in)

b) What is the max height of the ball?
c) How far did the ball land from Scott?
d) How long was the ball in the air?


Calculator problem if that wasn't obvious enough.




Formulas:

x(t) = (V * cos x)t
y(t) = -0.5gt^2 + (V * sin x)t + h




My attempts: (which are wrong by the way)

a)
x(t) = (50 * cos 65)t [CORRECT]
y(t) = -0.5(9.8)t^2 + (50 * sin 65)t + 3 [ITALICIZED PART IS WRONG; I figured g stood for gravity, so 9.8, right?]

b)
107.694 ft (didn't get formula right, and probably didn't use calculator correctly, so these are probably far off)

c)
190.178 ft.

d)
Didn't have enough time to finish.





This is a pretty quick PreCalc problem if you know what you're doing (which I didn't), so it would really help if one could do this.

And if one could tell me what mode settings my TI-83 should be on when I do this, I'd appreciate it.
 

Answers and Replies

cristo
Staff Emeritus
Science Advisor
8,056
72
Scott kicked a football with an initial velocity of 50 ft/sec at an angle of 65 degrees with the horizontal and at a height of 3 feet. Write the equations that would model this situation and answer the following:

a)
x(t) = _____________ (fill in formula with variable values plugged in)
y(t) = _____________ (fill in formula with variable values plugged in)

b) What is the max height of the ball?
c) How far did the ball land from Scott?
d) How long was the ball in the air?


Calculator problem if that wasn't obvious enough.




Formulas:

x(t) = (V * cos x)t
y(t) = -0.5gt^2 + (V * sin x)t + h




My attempts: (which are wrong by the way)

a)
x(t) = (50 * cos 65)t [CORRECT]
y(t) = -0.5(9.8)t^2 + (50 * sin 65)t + 3 [ITALICIZED PART IS WRONG; I figured g stood for gravity, so 9.8, right?]
Those equations look fine to me; what part did you mean to put in italics?

b)
107.694 ft (didn't get formula right, and probably didn't use calculator correctly, so these are probably far off)

c)
190.178 ft.

d)
Didn't have enough time to finish.
I can't check your answer if you don't give any working! You will need to work through the algebra by hand, and not just quote what your calculator tells you.

This is a pretty quick PreCalc problem if you know what you're doing (which I didn't), so it would really help if one could do this.
I'm afraid we don't do homework for students here at PF, but rather offer guidance once the student has made an attempt on his or her own.
 

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