Trajectory

[The3point14]

I have had a few problems with trajectories lately, any help would be greatly appreciated.

The first comes from the study list, question 03B-77.

A water skier is pulled over a ramp by a boat going 30 mph. If the ramp has a launch angle of 25(deg) and maximum height of 4ft above the water, how far from the end of the ramp does the skier hit the water if he lets go of the rope as he leaves the ramp. The skiers velocity remains 30mph.

Also I found this question in the Practice Manual for S&G

02D-57

A football player punts a football 52 yards with a hang time of 4.3 s. What was the initial velocity of the football?

I thought this would leave to many different [ veloctiy / angle ] answers, using vh= Velocity * time * cos(x), but the answer is 53.3 mph.

[bradp]

[AuSmith]

You can condense these into formulas. If you fire a projectile at angle [unparseable or potentially dangerous latex formula] and initial velocity [unparseable or potentially dangerous latex formula]...

[unparseable or potentially dangerous latex formula]

[unparseable or potentially dangerous latex formula]

and

[unparseable or potentially dangerous latex formula]


[unparseable or potentially dangerous latex formula] corresponds to when the projectile reaches the same height at which it was thrown.... So, there is a minor problem with the ramp problem. Sometimes, calc apps expects to consider small differences like the ramp and sometimes not. Why can't we be consistent??

[bradp]

shorter solution edited in

[The3point14]

Thank you guys for the replies, chances are that I will have a few more questions for you before next weekend, although they probably won't be regarding trajectory, I will post them here

[bradp]

solution to this problem?

[unparseable or potentially dangerous latex formula] A basketball basket is 18 in wide and the three point line is 20 ft 6 in from the center of the basket. If the basket is 3 ft above the point of release of the basketball, what shooting angle frm the three-point line does this represent if the 9-in diameter ball does not hit the rim as it goes in?
Answer: [unparseable or potentially dangerous latex formula] degrees... doesn't seem realistic

[stupidityismygam]

solution: a) skip it
b) get a pair of scissors, cut it out, crumple into a ball, shoot a 3-pointer with it

you choose

[NickR]

Isn't that bad...you need to use the equation [unparseable or potentially dangerous latex formula]

First if you think about it, two basketballs can fit into the net (technically) so the center of the basketball can be anywhere from 4.5 inches to the left of the center of the net to 4.5 inches to the right(since radius is 4.5 inches). This makes for a total distance of 9 inches of leeway and that value is also [unparseable or potentially dangerous latex formula]. Next, your radius is simply the distance from the shooter to the goal - [unparseable or potentially dangerous latex formula] inches. Substitute into the equation and you'll get [unparseable or potentially dangerous latex formula].

[AuSmith]

What about backboard?

[NickR]

I think they just want side to side shooting angle without the inclusion of the backboard or other factors.

[bradp]

could have been worded better

[Kurt]

Yeah, it could have been. After reading the question, I thought it wanted the trajectory angle...a vertical angle instead of a horizontal one.