Find initial velocity and time in the air- projectile motion

In summary, the soccer ball was kicked at 38.0° with respect to the horizontal and traveled 64.0m before striking the ground. Using the given equations, its initial velocity was calculated to be 3.14m/s and it was in the air for 7.96 seconds. However, it may be more accurate to use the highest point it reaches and energy conservation to determine the initial velocity.
  • #1
dani123
136
0
1. Homework Statement

A soccer ball is kicked at 38.0° with respect to the horizontal and travels 64.0m before striking the ground.
a) what is its initial velocity?
b) how long was it in the air?

2. Homework Equations

dv=1/2*at2
dh=Vh*Δt
Kinetic equation d=Vi*t+ 1/2*at2
dh=-V2*sin2θ /g
sinθ=opp/hyp
cosθ=adj/hyp
Δt=-2Vsinθ / g

3. The Attempt at a Solution

a) dh=cos(38)*64m= 50.4m
dv=sin(38)*64m=39.4m

Find t=√(39.4m/(0.5*9.8))=7.96s

plug this value into the d=Vi*t+ 1/2*at2 equation and solve for Vi if d=64m

Vi=3.14m/s

b) V=dh/Δt= 50.4m/7.96s=6.33m/s

Then solve for Δt=-2Vsinθ / g= 0.80s

I would like for someone to just double check my answers and that I used the appropriate equations and that the number of significant figures are being respected! Thanks so much in advance!
 
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  • #2
Sorry, last answer is bad, it looks okay. I would consider the highest y it takes and use energy conservation(kinetic energy) to obtain the initial velocity
 
Last edited:

Related to Find initial velocity and time in the air- projectile motion

1. How do you calculate initial velocity in projectile motion?

The initial velocity in projectile motion can be calculated using the formula: v0 = vf - at, where v0 is the initial velocity, vf is the final velocity, a is the acceleration, and t is the time. You can rearrange the formula to solve for v0.

2. How do you find the time in the air for a projectile?

To find the time in the air for a projectile, you can use the formula: t = 2v0/g, where t is the time, v0 is the initial velocity, and g is the acceleration due to gravity. This formula assumes that the projectile is launched at ground level and lands at the same level.

3. Can you find the initial velocity and time in the air without knowing the angle of launch?

Yes, you can find the initial velocity and time in the air without knowing the angle of launch by using the range formula: R = v02sin(2θ)/g, where R is the range, v0 is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity. You can rearrange the formula to solve for v0 and t without knowing θ.

4. How does air resistance affect the initial velocity and time in the air of a projectile?

Air resistance can decrease the initial velocity and increase the time in the air of a projectile. This is because air resistance acts in the opposite direction of the projectile's motion, slowing it down and reducing its range. To account for air resistance, you can use a more complex formula that takes into consideration the projectile's mass, cross-sectional area, and drag coefficient.

5. Can you use the same formula to find initial velocity and time in the air for all types of projectiles?

The same formula can be used to find initial velocity and time in the air for all types of projectiles that follow a parabolic trajectory, such as a ball thrown or a bullet shot. However, for projectiles with non-parabolic trajectories, such as a rocket or a bullet fired at a high angle, different formulas must be used to calculate their initial velocity and time in the air.

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