Projectile Motion Lab: Understanding Speed and Trajectory

[cubs_fanatic]

1. if two projectiles have the same range must they ahve the same intial speed?

2. if the maximum altitudes of two projectiles are the same, must they have the same intial speed?

3. if two projectiles have the same range must they have the same time of flight?

4. two people are standing at the edge of a cliff. one throws a ball straight up and the other throws an identical ball straight down. the initial speds of the two balls are the same
A) which ball will have the larger speed when it lands? Explain.
B) which ball will have the larger average speed for the time interval it is in the air? Explain.

5. two pojectiles have the same intial speed and the same amount of time in the air. what other features of their trajectories are also the same? Explain.
20 minutes ago - 4 days left

 

[tiny-tim]

Welcome to PF!

Hi cubs_fanatic! Welcome to PF!

You can solve all these by using the standard constant acceleration equations.

Show us how far you get, and where you're stuck, and then we'll know how to help!

Have a go at #1 first ​

 

[cubs_fanatic]

well for the first one i think the range is a displacement in the x component of velocity. the x-component of velocity does not change during the flight of the projectile. If the initial speed is the same, the range will have to be also.

 

[tiny-tim]

Hi cubs_fanatic!

(btw, no need to pm me … everyone automatically gets email notification of any new post in any thread they're involved in )

well for the first one i think the range is a displacement in the x component of velocity. the x-component of velocity does not change during the flight of the projectile. If the initial speed is the same, the range will have to be also.

No, that doesn't follow.

Yes, the range is a displacement in the x direction, but it doesn't only depend on the x-component of velocity, it depends on both components.

Do the two equations, for the x and y components separately, for a final distance r, an initial speed v and an initial angle θ …

what do you get? ​

 

[cubs_fanatic]

how can i do the x and y components if i have no numbers to put into the equations. i don't understand this!

 

[tiny-tim]

how can i do the x and y components if i have no numbers to put into the equations. i don't understand this!

I gave you the numbers …

they're r v and θ ​

 

[denverdoc]

try doing the problem generally. Assuming no drag, the time to ascent is given by

V*sin($$\vartheta$$)/g where g=9.8 and V= velocity

range is given by time x horizontal velocity; note that time here is twice that of the ascent.

recall sin(2$$\vartheta$$)= 2 sin($$\vartheta$$)*cos($$\vartheta$$)

should allow you to develop a general eqn for range in terms of V and $$\vartheta$$

I'll leave the rest to you...

 

[cubs_fanatic]

I have not learned anything about projectiles and was given this worksheet to see what I know from studying vectors. I do not know what these equations i am given are for. Based on diagrams on the sheet of paper i have i am supposed to respond with "yes' or "no" to the questions. and the equations are not necesarry.

 

[denverdoc]

Fine, let's approach it w/o any math:

What is the range of a projectile shot vertically at high speed--say a gun? Now assume its just a tad off vertical and lands a few feet away. Any other way to lob the bullet the same distance?

 

[cubs_fanatic]

i was thinking if a car went 5m/s and wanted to end up at a train station it would end up there at the same range of another car going 5m/s.

 

[denverdoc]

You're thinking in straight lines, projectiles in this question generally refer to objects shot at an angle like a cannon. The range is the distance the from the cannon the ball lands.

 

[tiny-tim]

I have not learned anything about projectiles and was given this worksheet to see what I know from studying vectors. I do not know what these equations i am given are for. Based on diagrams on the sheet of paper i have i am supposed to respond with "yes' or "no" to the questions. and the equations are not necesarry.

ah, it would have been better if you'd told us that at the start

ok … does that mean you don't know about equations like v² = u² + 2as ?

i don't see how you can do this only with vectors …

have you done derivatives of vectors (dv/dt etc) ?

or conservation of energy (KE + PE = constant) ?