### Projectile Motion Experiment**Scenario:**Scientists are experimenting with a kind of gun that may eventually be used to fire payloads directly into orbit. In one test, this gun accelerates a 7.0-kg projectile from rest to a speed of \( 2.7 \times 10^3 \) m/s. The net force accelerating the projectile is \(8.2 \times 10^5\) N. The problem asks to determine the amount of time required for the projectile to come up to speed.**Given Data:**- Mass of the projectile: \( 7.0 \) kg- Final speed of the projectile: \( 2.7 \times 10^3 \) m/s- Net force applied to the projectile: \( 8.2 \times 10^5 \) N**Formula to Use:**The equation \( F = ma \) relates force, mass, and acceleration. We can rearrange this equation to solve for acceleration (\(a\)):\[ a = \frac{F}{m} \]Once we have the acceleration, we can use kinematic equations to find the time (\(t\)). Since the projectile starts from rest, we use:\[ v = at \]where \( v \) is the final velocity and \( t \) is the time.Rearranging to solve for time:\[ t = \frac{v}{a} \]**Solution Steps:**1. Calculate the acceleration:\[ a = \frac{F}{m} = \frac{8.2 \times 10^5 \text{ N}}{7.0 \text{ kg}} = 1.17 \times 10^5 \, \text{m/s}^2 \]2. Calculate the time:\[ t = \frac{v}{a} = \frac{2.7 \times 10^3 \text{ m/s}}{1.17 \times 10^5 \, \text{m/s}^2} \approx 0.023 \text{ s} \]**User UI:**- The input text box shows the answer: **0.023**.- The dropdown menu below the input box selects the unit of measurement, in this case, **seconds (s)**.- The system provides a hint section, although this hint is not visible in the current image

Mass of projectile is Initially projectile is at rest.Final speed of projectile is Net force on the…

Scientists are experimenting with a kind of gun that may eventually be used to fire payloads directly into orbit. In one test, this gun accelerates a 7.0-kg projectile from rest to a speed of 2.7 x 103 m/s. The net force accelerating the projectile is 8.2 x 105 N. How much time is required for the projectile to come up to speed?

Scientists are experimenting with a kind of gun that may eventually be used to fire payloads directly into orbit. In one test, this gun accelerates a 7.0-kg projectile from rest to a speed of 2.7 x 103 m/s. The net force accelerating the projectile is 8.2 x 105 N. How much time is required for the projectile to come up to speed?

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter9: Statics And Torque

Section: Chapter Questions

Problem 38PE: You have just planted a sturdy 2-m-tall palm tree in your front lawn for your mother's birthday....

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