Projectile Motion- Object Launched in the Air

In summary, the spring toy is launched from the ground at 2.3 m/s at an angle of 78° to the ground. The maximum height reached by the spring toy is 0.26 meters [up], found using the formula for displacement without time. The total time the toy was airborne is 0.46 seconds.
  • #1
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Homework Statement


A spring toy is launched from the ground at 2.3 m/s at an angle of 78° to the ground.
What is the maximum height reached by the spring toy?

Homework Equations


## \vec v_1v = \vec v_1 sin\Theta##

## \Delta \vec d = \vec v_1v \Delta t + \frac 1 2 \vec a \Delta t^2##

The Attempt at a Solution



## \vec v_1v = 2.3 m/s [up] (sin78 degrees)
\\ = 2.25 m/s [up]##

## \Delta \vec d = \vec v_v1 \Delta t + \frac 1 2 \vec a \Delta t^2
\\ 0 = (2.25 m/s [up]) \Delta t + \frac 1 2 (-9.8 m/s^2) \Delta t^2
\\ 0 = \Delta t (2.25 m/s - 4.9 m/s^2) \Delta t
\\ \Delta t = 0.46 seconds##

That's the total time it was airborne. Maximum height is half that so 0.46/2 = 0.23 s.

Now to find the height.

## \Delta \vec v = \vec v_1 \Delta t + \frac 1 2 \vec a \Delta t^2
\\ = (2.25 m/s) (0.23 s) + \frac 1 2 (-9.8 m/s^2) (0.23)^2
\\ = 0.52 - 0.26
\\= 0.26 m [up]##

The max height is 0.26 meters [up].

I've followed my textbook's lead of rounding to two significant places through the work.

Am I correct at all?
 
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  • #2
Everything looks good to me. Personally, I keep the intermediate answers, in my calculator, to full digits, then round at the end.
 
  • #3
Thank you. Yeah, overall, the textbook isn't the greatest, but I'm just following its lead for this course.
 
  • #4
You were not asked for the time. You can get to the height directly by using the right SUVAT formula. Which one does not involve time?
 

FAQ: Projectile Motion- Object Launched in the Air

What is projectile motion?

Projectile motion is the motion of an object that is launched or thrown into the air and moves along a curved path due to the influence of gravity.

What factors affect projectile motion?

The factors that affect projectile motion include the initial velocity, angle of launch, air resistance, and the force of gravity.

How is the trajectory of a projectile determined?

The trajectory, or path, of a projectile is determined by the initial velocity and angle of launch. It follows a curved path known as a parabola.

What is the range of a projectile?

The range of a projectile is the horizontal distance it travels before hitting the ground. It is determined by the initial velocity and angle of launch.

How does air resistance affect projectile motion?

Air resistance, also known as drag, can slow down a projectile and affect its trajectory. It is dependent on the shape and size of the object and the density of the air.

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