2 dimension kinematics Cutnell Chapter 3 Prob 26

[Jacque77]

Homework Statement

A quarterback claims that he can throw the football a horizontal distance of 184 m. Furthermore, he claims that he can do this by launching the ball at the relatively low angle of 29.7 ° above the horizontal. To evaluate this claim, determine the speed with which this quarterback must throw the ball. Assume that the ball is launched and caught at the same vertical level and that air resistance can be ignored. For comparison a baseball pitcher who can accurately throw a fastball at 45 m/s (100 mph) would be considered exceptional

Homework Equations

.5*184m=92m -adjacent side
90-29.7(theta)=60.3 other angle
Hyp=x/cos theta or 91.42=92/.8686
Opposite ; tan theta=X/92(adjacent side)=54.27 is (.5704*92)

need time so d=(.5)at^2
184=(.5)(-9.80)(t)^2 =-6.13seconds

The Attempt at a Solution

see above - I'm not sure I have the time set up properly. I need a hint as to how to get
started with determining the velocity - just a hint!

 

[stewartcs]

Use an equation for Projectile Motion instead.

 

[fikus]

Split the velocity vector on x and y component. Then it's easy to calculate the time of flight since x speed is constant. Once you have time, you have tu calculate what initial y speed should be that the vertical throw with that speed would be that long.

 

[stewartcs]

Assume that the ball is launched and caught at the same vertical level and that air resistance can be ignored

Since the problem is stated this way, the horizontal displacement is the range. Thus, use a projectile motion equation for the range.

It will then be a very simple problem of substituting in the given values!