What you know about math?

 


 

 

Projectile Motion
St. Mary's H.S. Physics

 

 

 

 

 

 

 

 

Vx
(m/s)		 Vy
(m/s)
25 40
25 30
25 20
25 10
25 0
(peak)
25 -10
25 -20
25 -30
25 -40

 


 

 

4. Word Problems

 

www.sihunt.co.uk Russian long jumper Tayana Lebedeva performs a double hitch action in the 2007 world finals in Osaka Japan.

 

Ex) An athlete doing a running jump leaves ground at an angle of 25.° and a velocity of 10. m/s.

(a) What is the initial vertical component (Viy) of the athlete's velocity?

 

Ex)  An athlete doing a running jump leaves ground at an angle
 of 25.° and a velocity of 10. m/s.

 

(a) What is the initial vertical component (Viy) of the athlete's velocity?

                   

 

 

 

Viy = VsinӨ

 

 

 = (10. m/s)sin25.

 

 

 

= 4.2 m/s

 

 


 

 

(b) How long does it take for
the athlete to reach her maximum height?

 

 

 

 

 

 (b) How long does it take for
the athlete to reach her maximum height?

 

 

 

X Y
t = ? Viy = 4.2 m/s
(from above)
 
t  =  ?
  Vfy= 0
(peak)
 
ay = -9.8 m/s2

 

 

Vf = Vi + at

 

 

0 = 4.2 m/s + (-9.8 m/s2)t

 

 

- 4.2 m/s = (-9.8 m/s2)t

 

(- 4.2 m/s)/(-9.8 m/s2) = t

 

 

 

t = .43 secs
 to reach peak

 

 

 

 

 

 

(b) How long did it take for the athlete to complete the entire jump?

 

 

 

 

 

 

(b) How long did it take the athlete to complete the entire jump?

 

 

 

 

Total time =
double
peak time

 

 

 

Entire Jump:

 


total time = .86 seconds

 

 

 

 

(c) How far did she jump?

 

 

 

dx = ?

 

 

 

(c) How far did she jump?

 

dx = ?

t = .86 sec

 

dx = Vxt

 

 

(Must find Vx first)

 

Vx = VcosӨ

 

 

Vx = (10. m/s)cos25.

 

Vx = 9.1 m/s

 

Vx = VcosӨ

 

dx = 9.1 m/s(.86 sec)

 

 

 

dx = 7.8 m

 

 

 

 

 

 

Ex) A projectile leaves ground at an angle of 60.° and a speed of 100.m/s.

(a) Find the initial vertical component of the object's velocity

 

Ex) A projectile leaves ground at
an angle of 60.° and a speed of
100. m/s.

 

(a) Find the initial vertical component of the object's velocity 

 

 

Ө = 60.°

 

Vi  = 100. m/s

 

 

Viy = Vi(sinӨ)

 

 

= (100. m/s)sin60.°

 

 

 

 

Viy = 87. m/s

 

 

 

 

 

 

 

 

 

(b) Find the objects maximum height.

 

Viy = 87. m/s
ay = -9.8 m/s2
dy (max) =?
Vfy = 0 (at max height)

 

 

Vf2 = Viy2 + 2ad

 

 

02 = (87. m/s)2 + 2(-9.8 m/s2)d

 

0 = 7569 + -19.6dy

 

 

-7569 = -19.6(dy)

 

 

dy = 386 m

 

 

Actually ......

 

 

 

dy = 390 m

(correct sig. figs)

 

 

 

ex) A rock is thrown from a cliff with initial speed of 40. m/s at an angle of 45.° below  the horizontal. 

(a) What is the vertical component of the initial velocity?

a) What is the vertical component
of the initial velocity?

 

 

Ө = 45.°

 
Vi = 40. m/s
     
 
Viy = VsinӨ
 
= (40. m/s)sin45.° 

			
 

			
Viy = 28 m/s

		

		
 

		
 

		

		 

		

		

		

		 

		

		 

		
 

		
(b) If the 
		rock strikes ground in 1 sec what is height of cliff?
		

		
 

		

		 

		

		 

		

		

		

		 

		

		 

		
 

		
(b) If the 
		rock strikes ground in

		 1.0 sec what 
		is 
		height of cliff?

		
 

		
a = + 9.8 m/s2

		
 

		
t = 1.0 sec

		
 

		
Viy = 28 m/s
		(from before)

		

		
dy = ?

		
 

		
 

		
dy = Viyt + (½)at2

		
 

		
 

		
 

		
 

		
 

		

			

				
=28.m/s(1sec)+½(9.8m/s2)(1.0sec)2

			

		

		
 

		
 

		
 

		
28 m + 4.9 m

		
 

		

		
 

		
dy = 33 m

		

		
 

		
 

		

		
 

		
 

		

		

		 

		

		
 

		

		 

		

		 

		

		

		

		 

		

		 

		
 

		

		At peak,

		
 

		
 Vy = ?, Vx 
		= ?

		
 

		
 

		
 

		

		
 

		
 

		
 

		
Vy = 0, 

		Vx 
		= 9.0 m/s

		
 

		

		 

		

		

		
 

		
 

		
h

		

		 

		

		Total Time in Air?

		

		 

		

		 

		

		 

		

		1.84 sec 

		(twice peak)

		

		 

		

		 

		

		actually 1.8 (sig figs)

		

		 

		

		 

		

		

		

		 

		

		 

		

		 

		

		

		

		dx = ? 

		

		 

		

		

		

		dx = Vxt

		

		 

		

		

		
dx = (9.0 m/s)1.84 
		sec

		

		
dx = 16.56 m

		

		
 

		
 or 17 m

		

		
Correct Significant figures

		
 

		
 

		

			

		

			

		

		

		
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