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

1 Answer
Apr 25, 2018

The time is =1.06s

Explanation:

The equation describing the trajectory of the projectile in the x-y plane is

y=xtantheta-(gx^2)/(2u^2cos^2theta)

The initial velocity is u=3ms^-1

The angle is theta=(1/3pi)rad

The acceleration due to gravity is g=9.8ms^-2

The distance y=0

Therefore,

xtan(1/3pi)-(9.8*x^2)/(2*3^2cos^2(pi/3))=0

1.732x-1.089x^2=0

x(1.732-1.089x)=0

x=0, this is the starting point

x=1.732/1.089=1.59m

The time is t=x/v_x=1.59/(3cos(pi/3))=1.06s