Question

A daredevil is shot out of a cannon at 51.7 ◦ to the horizontal with an initial speed of 31.9 m/s. A net is positioned a horizontal distance of 39.1 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:30.34 m

Step-by-step explanation:

Given

launch angle
`=51.7^(\circ)`

Initial velocity u=31.9 m/s

Position of net = 39.1 m

We know equation of trajectory of a projectile is

`y=x\tan \theta -(gx^2)/(2u^2(\cos \theta )^2)`

`y=39.1* \tan 51.7-(9.8* 39.1^2)/(2* 31.9^2* (cos51.7)^2)`

`y=49.509-(9.8* 1.502)/(2* 0.384)`

`y=49.509-(14.719)/(0.768)`

`y=49.509-19.165=30.343 m`

Therefore Net should be placed 30.34 m above ground