Question

A daredevil is shot out of a cannon at 31.4 ◦ to the horizontal with an initial speed of 25.9 m/s. A net is positioned a horizontal distance of 39.7 m from the cannon. At what height above the cannon should the net be placed in order to catch the daredevil? The acceleration of gravity is 9.8 m/s 2 . Answer in units of m.

Answer 1

Answer:

The net should be placed at a height of 8.45 m

Explanation:

In order to calculate the height you have to apply the equations of projectil motion.

For x-axis, the position at a time t is given by:

Xf=Xo +(VoCosα)t (I)

Where Xf is the final position, Xo is the initial position, Vo is the initial speed and t is the time.

For the y-axis, the position at a time t is given by:

Yf=Yo + (VoSinα)t - 0.5g$t^{2}$ (II)

Where Yf is the final position, Yo is the initial position, Vo is the initial speed, t is the time and g is the acceleration of gravity.

For both equations, ∝ is the angle formed by the cannon and the horizontal

The height where the net should be placed in order to catch the daredevil is given by replacing the time when the daredevil will be in the horizontal position of 39.7 m in the equation of position for the y-axis.

So, you have to calculate the time using (I)

Let the system of reference be placed at x=o and y=o

Xf= 0 + 25.9Cos(31,4◦)t

Xf=39.7

39.7=22.1t

Dividing both sides by 22.1 to find the value of t:

t=1.79 seconds

Replacing the time in equation (II) to find the height:

Yf=0 +25.9Sin(31,4◦)(1.79) - 0.5(9.8)$1.79^{2}$

Yf= 8.45 m

So the height is 8.45 m