Projectile shot and dropping object.

[Whateverchan]

1. The height (in meters) of a projectile shot vertically upward from a point 4 m above ground level with an initial velocity of 25.5 m/s is h = 4 + 25.5t − 4.9t^2 after t seconds. (Round your answers to two decimal places.)

So, I found its velocity, maximum height, and how long it takes to reach the maximum height. What I have to do now is find out when it would hit the ground and with what velocity.

For how long it would hit, I am supposed to set 4 + 25.5t − 4.9t^2 = 0, and solve for t. But I am not sure how to tackle this one, because all problems I've seen only have a number with t^2 and another constant. That 25.5 throws me off. As for velocity, I think I just to plug the new found t into the original equation. What do I do?

2. A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s. Find the rate at which the area within the circle is increasing after each of the following. 1s, 3s, 7s.

I found the derivative of the area of the circle to be 2pi r. I just have to multiply 60 with the number of seconds, and plug it into the derivative, correct? Well I tried that, for example, 1s would be 120pi or 277, and they both came out wrong. What did I miss?

 

[stapel]

1. ...I am supposed to set 4 + 25.5t − 4.9t^2 = 0....

So plug the coefficients into the Quadratic Formula that you memorized back in algebra, and simplify to find the t-values.

2. A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s. Find the rate at which the area within the circle is increasing after each of the following. 1s, 3s, 7s.

I found the derivative of the area of the circle to be 2pi r.

Do you mean that you set up the functional relation as A = (pi)r^2, so the derivative, with respect to time t, was given by dA/dt = 2(pi)r(dr/dt)?

I just have to multiply 60 with the number of seconds, and plug it into the derivative, correct?

Do you mean that you evaluated r(t) = 60t at t = 1, and then plugged this value (namely, r(1) = 60) into the derivative and solved for dA/dt? So you got dA/dt = 2(pi)(60)(60)? (And then of course I'd put units on the final numerical value.)

Well I tried that, for example, 1s would be 120pi or 277, and they both came out wrong. What did I miss?

How did you arrive at this value? Please reply showing your work, similar to how I did above. Thank you.

 

[wjm11]

1. The height (in meters) of a projectile shot vertically upward from a point 4 m above ground level with an initial velocity of 25.5 m/s is h = 4 + 25.5t − 4.9t^2 after t seconds. (Round your answers to two decimal places.)

So, I found its velocity, maximum height, and how long it takes to reach the maximum height. What I have to do now is find out when it would hit the ground and with what velocity.

...As for velocity, I think I just to plug the new found t into the original equation.

Your given equation solves for h, which is displacement. You need to solve for velocity, v = dh/dt. So, take the derivative of h = 4 + 25.5t − 4.9t^2; then you'll have the velocity equation.