This physics problem is driving me crazy, and I still can't figure it out!!!?

Question

A delivery boy needs to know his projectile motion to throw a paper horizontally from a height of 1.40m to a door that is 13.5m away. What must the paper's velocity be for it to reach the door?

I tried using motion equations to solve this problem. I feel as if the problem isn't giving me enough information for it to be solved. Please help me if you can! Thank you!!

Answer 1

The information are sufficient.

R=u*root over(2h/g)
where, R=horizontal range
u=horizontal velocity
h=height
g=9.8m/s sq

Now, 13.5=u*root over(2*1.4/9.8)

On simplification you will get, u=25.28 m/s. Thts all.

Answer 2

It works out to be the correlation of two motions. One is horizontal motion, described by x=vt, the other is vertical motion, described by y=(gt^2)/2, where g = 9.8 m/s^2. You are using the property that t is equal in both equations. Use t = x/v, plug into the equation for y, use x = 13.5 m and y = 1.40 m, then solve for v, which would be the velocity that you are solving for.

Answer 3

First calculate the time for the paper to reach the ground, if it is simply made to fall down.

S = (½) g t^2. Or t^2 = 2s /g = 2x 1.4 /9.8 = 0.2857142 second^2; t = 0.5345224s
In the ground it has to travel a distance of 13 .5 m.

Suppose it takes a time of 0.5345224s second to cover this distance of 13 .5 m.

Then its speed is given by 13 .5 m/ 0.5345224s second = 25.26 m/s.

Now when you throw the paper horizontally with a speed of 25.26 m/s, it falls to the ground as well as moves horizontally, since the motion takes place during the same interval of time of t = 0.5345224s

Answer 4

First you should realize that the horizontal and vertical motions are independent. The vertical motion is governed by the acceleration due to earth's gravity. The equation you are supposed to use is d= 1/2*g*t^2. Solving for t gives you: t = square root of 2*d/g = square root of 2*1.4/9.8 = 0.5345 (where 9.8 is the acceleration due to earth's gravity at sea level in meters per second square. 0.5345 is the time, in seconds, it will take the newspaper to drop 1.4 meters. In that time, the newspaper has to travel 13.5 meters, so the initial velocity of the newspaper has to be v = d/t, that is 13.5/0.55345 = 25.26 meters per second which is about 82.87 feet per second, which is about 56.5 miles per hour. I have, of course, neglected air resistance and assumed the newspaper to behave as a point mass. Hope I have helped you! Let me know!
Pavi

Answer 5

The above solution will assume a launch angle of 0 degrees, as if the paper boy were to fire off the projectile from a high power cannon. Realistically he would toss it at an angle, which would alter the velocity. For the sake of homework, the above way works.

Answer 6

This is how you solve it:

Find out how long it takes the paper to fall 1.4m. Use known gravitational acceleration and acceleration formulas to find that number.

The paper must travel 13.5 meters in that time. You know the distance and the time, so you can figure the velocity needed.

Answer 7

The time that it takes the paper to start from rest and fall the distance of 1.40 meters is the flight time. In that time it has to cover the 13.5 meters.

Vectors are independent, so the falling part of the trip is independent of the horizontal part.

Answer 8

Have you drawn a vector diagram? That would be my first step.

Answer 9

i think that you may have to allow for gravity and then work out the difference.