How to find initial velocity in projectile motion problem?

In summary, the conversation discusses a problem involving projectile motion. The problem asks for the initial velocity of a spear thrown at a 35 degree angle, with a total horizontal distance of 201.24 meters. The conversation also covers using equations from a projectile chapter to find the initial velocity and the trigonometry and algebra involved in solving the problem. Finally, the conversation includes notes on projectile motion and a similar problem involving a cannon firing a ball at the top of a cliff. The solution involves finding the velocity using equations for horizontal and vertical distance.
  • #1
nicoleisgoat
5
0
I'm in a physics 1 honors course at my high school and we have been working on projectile motion problems. I'm very confused on how to solve this problem though more because of the math than the physics I think.

The problem asks for the initial velocity of a spear that was thrown at a 35 degree angle with respect to the horizontal. The only other information given is that the spear was thrown a total horizontal distance of 201.24 meters.

I first used the equation dy=Viyt+1/2ayt2 and eventually came to t=Visin35/4.9

after that i plugged it into the same equation but for the x components and got as far as:
201.24=Vicos35(Visin35/4.9)

what do I do after that to solve for Vi?
 
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  • #2
In the projectile chapter, you will find three expressions. One for maximum height, second for time flight and third for range of the projectile. Use the third formula to find the initial velocity.
 
  • #3
..which projectile chapter?
 
  • #4
In any physics textbook can you find the equations of projectile motion?
 
  • #5
no, my teacher isn't teaching it from a textbook. we just learned to use galileo's equations for motion but break them into x and y..
I know for certain that we are expected to use the d=Vit+1/2at2 equation first with y components to find t and then plug that in. I'm just not sure what to do once i plugged it in.
I guess my question is more related to the trig/algebra involved in finding the solution
 
  • #6
Substitute the values of sin35 and cos35 and solve for Vi.
 
  • #7
what do you mean substitute the values?
 
  • #8
201.24=Vicos35(Visin35/4.9) = Vi*2(sin35)(cos35)/4.9. Find the values of sin 35 and cos35 and put it in the above equation to get Vi.
 
  • #9
thank you soooo much! I finally got it (:
 
  • #10
is the Vi 14.47?
 
  • #11
Some basic notes--

One nice thing about projectile motion is that the horizontal motion and vertical motion are independent of one another. Once thrown, the projectile has constant velocity in the x direction (acceleration in the x direction is zero). Its velocity in the y direction is effected by gravity (if you're using toward Earth as your negative y direction, a_y roughly equals -9.8 m/s^2).

If you know the angle of the initial velocity, you can find the x and y components by drawing a right triangle with v_0 as the hypotenuse (the magnitude of the velocity will be the length of that side). Sometimes you will know know the magnitude right away, so you need to think about what x and y are in terms of trig functions. The way many simple projectile motion problems are set up, the x component is simply v_0*cos(theta) and the y component is v_0*sin(theta). (It depends on your coordinate system and what angle(s) were given.)
 
  • #12
Just wondering is the 4.9 in the first equation the vertical distance or how did that get there? I have a similar problem:A cannon is firing a ball at the top of a cliff.
What is the velocity of the cannonball if the horizontal distance between the cannon and the base of the cliff is 1000 meters, the height of the cliff is 60 meters and the cannon makes a 53 degree angle with respect to the horizontal.

Thanks
 
  • #13
[tex]x=v_ocos\theta t[/tex]
[tex]y=y_o + v_ot - \frac {1}{2} g t^2[/tex]
Solve the first one for t and substitute into the second equation to find v.
 

1. What is projectile motion?

Projectile motion is the motion of an object that is propelled or launched into the air and then moves under the force of gravity. It follows a curved path known as a parabola.

2. Why is it important to find the initial velocity in projectile motion?

Knowing the initial velocity in projectile motion allows us to predict the trajectory and landing point of the object. It also helps in understanding the forces acting on the object and can be used to calculate other important parameters such as time of flight and maximum height.

3. What is the equation for finding initial velocity in projectile motion?

The equation for finding initial velocity in projectile motion is v0 = vx / cosθ, where v0 is the initial velocity, vx is the horizontal velocity, and θ is the angle of launch.

4. How do you solve for initial velocity in a projectile motion problem?

To solve for initial velocity in a projectile motion problem, you will need to have the values of at least two other parameters such as the angle of launch, horizontal velocity, time of flight, or maximum height. You can then use the equation v0 = vx / cosθ to calculate the initial velocity.

5. Can you find the initial velocity if the object is launched from an elevated position?

Yes, the initial velocity can still be calculated if the object is launched from an elevated position. In this case, the vertical velocity will also need to be taken into account. The equation for finding initial velocity in this scenario will be v0 = √(vx2 + vy2) / cosθ, where vx and vy are the horizontal and vertical velocities, respectively.

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