Finding time and final velocity

[physfall]

Homework Statement

A photographer in a helicopter ascending vertically at a constant rate of 12.5 m/s accidentally drops a camera out the window when the helicopter is 60.0 m above the ground.
-How long will it take the camera to reach the ground? What will its speed be when it hits?
a= -9.8 m/s^2 displacement=60 m

Homework Equations

(final v)^2=(initial v)^2 + 2*a*deltax
deltax=1/2a(t^2)+(initial v*t)

The Attempt at a Solution

initial v=0
so time will equal 3.5 s, and final velocity will equal 33.67 m/s^2
however, these are incorrect

 

[CompuChip]

The initial v is not 0, but the v of the helicopter and photographer. If you don't believe is, look up some movies of a ball shot from a moving car: when the car is moving at 50 km/h and the ball is shot backwards at 50 km/h, it drops straight down.

 

[tomcue]

calculations.



I would approach this problem by first identifying the relevant equations and variables. In this case, we are dealing with motion under constant acceleration, so the equations of motion for constant acceleration will be useful. The variables in this problem are the initial velocity (which is 12.5 m/s and is given), the final velocity (which we need to find), the acceleration (which is -9.8 m/s^2 due to gravity), and the displacement (which is 60 m and is given).

Using the equation (final v)^2=(initial v)^2 + 2*a*deltax, we can solve for the final velocity. Plugging in the values, we get (final v)^2 = (12.5 m/s)^2 + 2*(-9.8 m/s^2)*(60 m) = 1562.5 m^2/s^2. Taking the square root of both sides, we get the final velocity to be 39.5 m/s.

Next, to find the time it takes for the camera to reach the ground, we can use the equation deltax=1/2a(t^2)+(initial v*t). Plugging in the values, we get 60 m = 1/2*(-9.8 m/s^2)*(t^2) + (12.5 m/s)*(t). This is a quadratic equation, and solving for t using the quadratic formula, we get t = 4.04 s (rounded to the nearest hundredth).

Therefore, it will take 4.04 seconds for the camera to reach the ground and its speed will be 39.5 m/s when it hits.