Projectile Motion: Glider Release Speed and Time to Reach the Ground

In summary, the glider is tugged by an airplane at 81 m/s and experiences a constant acceleration of 2.4 m/s2 at 1.1° below the horizontal due to air drag. To find the time it takes for the glider to reach the ground 5.7 km below, we can use the equation y = y0 + v0y*t + 1/2*at^2 and set it equal to zero since y = 0 at ground. We can also use the equation for the y component of acceleration and solve for t. The correct answer is 4.8 s (c).
  • #1
Delta G
5
0

Homework Statement



A glider is tugged by an airplane at 81 m/s when it is released. If the original speed was along the horizontal and the glider is now under a constant acceleration of 2.4 m/s2 at 1.1° below the horizontal due to air drag, how long will it take to reach the ground 5.7 km below?

a. 250,000 s
b. 500s
c. 4.8 s
d. 2.2s

Homework Equations



v0x = v0*cos(theta)
v0y = v0*sin(theta)
vy = v0y + at
x = x0 + v0x*t
y = y0 + v0y*t + 1/2*at^2
vy^2 = v0^2 +2a(delta y)

The Attempt at a Solution




No idea on how to start.
 
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  • #2
Notice that the horizontal components of acceleration and velocity do not affect the time it takes to travel vertically - the time to reach the ground.

y = y0 + v0y*t + 1/2*at^2

This equation should work. You know y, y0, v0, and a. Solve for t.
 
  • #3
How do I find the initial acceleration in the y direction?
 
  • #4
Delta G said:

Homework Statement



A glider is tugged by an airplane at 81 m/s when it is released. If the original speed was along the horizontal and the glider is now under a constant acceleration of 2.4 m/s2 at 1.1° below the horizontal due to air drag, how long will it take to reach the ground 5.7 km below?

a. 250,000 s
b. 500s
c. 4.8 s
d. 2.2s

Homework Equations



v0x = v0*cos(theta)
v0y = v0*sin(theta)
vy = v0y + at
x = x0 + v0x*t
y = y0 + v0y*t + 1/2*at^2
vy^2 = v0^2 +2a(delta y)

The Attempt at a Solution




No idea on how to start.

The force of air drag ([tex]F_{drag}[/tex]) on the glider is in the opposite direction of the velocity of the glider. Since this drag is 1.1 degree below the horizontal, the [tex]F_{drag}[/tex] will have a horizontal and vertical component (i.e. will pull the glider backward and downward). So to find the acceleration of the glider in the y direction, we find the resultant force acting on the glider, which is the sum of the y components of the forces acting on it (e.g. [tex]F_{grav}[/tex] and [tex]F_{drag}[/tex]).

[tex]F_{drag}[/tex] = 2.4 m/s2 at 1.1° below the horizontal
[tex]y_{i}[/tex] = 5.7 km = 5700 m
[tex]v_{i}[/tex] = 81 m/s

[tex]\sum[/tex]F = ma
[tex]\sum[/tex][tex]F_{y}[/tex] = [tex]F_{grav}[/tex] + [tex]F_{drag}[/tex] = m[tex]a_{y}[/tex]
[tex]\sum[/tex][tex]F_{y}[/tex] = -mg - [tex]F_{drag}[/tex]sin(1.1) = m[tex]a_{y}[/tex]
[tex]a_{y}[/tex] = -(g + ([tex]F_{drag}[/tex]sin(1.1))/m)

From the y component of acceleration, you can derive the y equation as xcvxcvvc said, set that equation equal to zero since y = 0 at ground, and solve for t.
 

FAQ: Projectile Motion: Glider Release Speed and Time to Reach the Ground

What is the definition of projectile motion?

Projectile motion is the motion of an object through the air under the influence of gravity. It follows a curved path, known as a parabola, due to the vertical and horizontal components of its velocity.

How does a glider experience projectile motion?

A glider experiences projectile motion when it is launched into the air and its wings generate lift, allowing it to stay airborne. As the glider moves through the air, it follows a curved path due to the effects of gravity.

What factors affect the trajectory of a glider in projectile motion?

The trajectory of a glider in projectile motion is affected by its initial velocity, the angle at which it is launched, and the force of gravity. Air resistance and wind can also play a role in altering the trajectory.

How can we calculate the maximum height and range of a glider in projectile motion?

To calculate the maximum height and range of a glider in projectile motion, we can use the equations of motion and the known initial conditions, such as the launch angle and initial velocity. These equations can be solved to determine the maximum height and range of the glider.

What are some real-world applications of understanding projectile motion in gliders?

Understanding projectile motion in gliders has various real-world applications, including in the design and engineering of aircraft and missiles, sports such as javelin throwing and long jump, and even the study of celestial bodies and their orbits. It also helps in predicting the trajectory of objects in projectile motion, which is crucial in fields such as ballistics and space exploration.

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