View source for Proj Motion EX 8

''Helena Dedic''

A plane flying horizontally dropped a supply of blankets for stranded hunters. The blankets landed 4 s after the drop with a speed of 50 m/s. <br>
 
a.	What were the components of the velocity when the supply landed? <br>
 

b.	What was the velocity of the plane? <br>
 

c.	How high was the plane flying? <br>
 

d.	How far did the blankets move in the horizontal direction? <br><br>
 
'''Solution:''' <br>
 

The plane is flying horizontally with some speed v. The blankets, when dropped, move (initially) with the speed of the plane. <br>
 
 Their initial velocity is therefore horizontal.
 
Now, let us choose coordinate system with origin on the ground just below the drop point. The positive y-axis points upward and the positive x-axis points in the direction the plane is moving. <br>
 
This means the y-component of initial velocity is 0 while the x-component is v. <br>
 
The blankets follow parabolic path, and land 4 s later. Since the y-component of velocity decreases at a rate of - 10 m/s every second we know that the blankets land with vertical component of velocity equal to - 40 m/s. Moreover, we are told the speed of the blankets as they land is 50 m/s. Thus we know the magnitude and y-component of velocity. Consider the following picture: <br>
 

[[image: Proj Motion Sol 8.png|TOP]] <br><br>

Thus let us draw <math>v_x</math> - t and <math>v_y</math> - t graphs and use these to solve the given problem:<br>


[[image: Proj Motion Sol 8b.png|TOP]] <br><br>

a.	We know the magnitude of velocity is 50 m/s and the y-component is - 40 m/s. We solve for vx using the equation : <br>
 <math>v^2 = v_x^2 + v_y^2</math> <br>

 <math>v_x^2 = 50^2 - 40^2 = 900</math> <br>

It follows that <math>v_x = 30 m/s</math>, so the components of velocity at impact is (30, -40) m/s.<br>
 

b.	The velocity of the plane is the same as the horizontal component of the velocity of the blankets i.e., 30 m/s. <br>
 

c.	The vertical distance travelled by the blankets is the area under the triangle: ½ • 4 • (- 40) = - 80 m. The vertical displacement of the blankets is - 80 m so the plane flies at an altitude of 80 m. <br>
 

d.	Since the horizontal velocity of the blankets was 30 m/s we conclude that they covered a horizontal distance of 120 m in 4 s.<br>
 
 


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