How High Will the Passenger Be When the Camera Reaches Her?

[mikep]

can someone help me with this problem?
A hot air balloon has just lifted off and is rising at the constant rate of 2.4 m/s. Suddenly, one of the passengers realizes she has left her camera on the ground. A friend picks it up and tosses it straight upward with an initial speed of 11.2 m/s. If the passenger is 2.5 m above her friend when the camera is tossed, how high is she when the camera reaches her on its way up?

i tried to first find the time, which i think is 0.88s. but I'm not sure. can someone please help

 

[NateTG]

can someone help me with this problem?
A hot air balloon has just lifted off and is rising at the constant rate of 2.4 m/s. Suddenly, one of the passengers realizes she has left her camera on the ground. A friend picks it up and tosses it straight upward with an initial speed of 11.2 m/s. If the passenger is 2.5 m above her friend when the camera is tossed, how high is she when the camera reaches her on its way up?

i tried to first find the time, which i think is 0.88s. but I'm not sure. can someone please help

Well at the time the height of the camera and the height of the baloon should be equal, right, so we can calculate both, and see if they're equal:

Tossed camera height after 0.88s:
$$11.2 (0.88) - \frac{1}{2} 9.81 \times 0.88^2 \approx 6$$
Ballon height after 0.88s:
$$2.5+2.4 (0.88) \approx 4.5$$

I'm not sure where your error is.
Calculating the time first should get you to the right answer.

If you're not sure how to proceed, you should be able to use what I wrote above to set up an equation.

 

[M98Ranger]

Sure, I'd be happy to help! To solve this problem, we can use the equation d = vt + 1/2at^2, where d is the distance, v is the initial velocity, t is the time, and a is the acceleration.

First, let's find the time it takes for the camera to reach the passenger. We can use the equation d = vt + 1/2at^2, where d is the distance, v is the initial velocity, t is the time, and a is the acceleration. In this case, the initial velocity is 11.2 m/s and the acceleration is -9.8 m/s^2 (since the camera is moving against the force of gravity). We also know that the distance the camera travels is 2.5 m. Plugging in these values, we get:

2.5 = (11.2)(t) + 1/2(-9.8)(t^2)

Solving for t, we get t = 0.56 seconds. This is the time it takes for the camera to reach the passenger.

Now, we can use the same equation to find the height of the passenger when the camera reaches her. In this case, the initial velocity is 2.4 m/s (since the passenger is already moving upward in the hot air balloon) and the acceleration is also -9.8 m/s^2. We also know that the time it takes for the camera to reach the passenger is 0.56 seconds. Plugging in these values, we get:

d = (2.4)(0.56) + 1/2(-9.8)(0.56^2)

Solving for d, we get d = 1.94 meters. This means that the passenger is 1.94 meters above her friend when the camera reaches her.

I hope this helps! Please let me know if you have any further questions or need clarification. Good luck with your homework!