A projectile is shot from the ground at a velocity of #23 m/s# and at an angle of #(3pi)/4#. How long will it take for the projectile to land?

1 Answer
Dec 18, 2016

Answer:

The total flight time of the projectile is #~~3.3s#

Explanation:

Assuming the launch and landing points are at equal altitudes, we can use a kinematic equation to determine the flight time from the launch of the projectile to its maximum altitude (#v_f=0#) and multiply by two to get the total flight time.

#v_f=v_i+a_yDeltat#

#=> Deltat=(v_f-v_i)/a_y#

#=>Deltat=(-v_i)/a_y#

We know that when an object is in free fall, the acceleration is equal to #-9.8m/s^2# (vertically).

Because the projectile is launched at an angle, we will need to break the velocity up into components. This can be done using basic trigonometry.

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Where #v# is the initial velocity, and #v_x# and #v_y# are the horizontal and vertical components of the velocity, respectively. We can see that:

#v_x=vcos(theta)#
#v_y=vsin(theta)#

We will only require the #y# component.

#v_y=23*sin((3pi)/4)= (23sqrt(2))/2m/s#

We can now calculate the rise time of the projectile.

#Deltat=(-v_i)/a_y#

#Deltat=(-(23sqrt(2))/2m/s)/(-9.8m/s^2)#

#Deltat=~~1.66s#

The total flight time is then #~~3.3s#