Model rocket with constant acceleration and lighthouse distance problem

[jwang023]

Homework Statement

Problem 1: A model rocket rises with constant acceleration to a height of 3.9 meters, at which point its speed is 28.0 m/s. How much time does it take for rocket to reach this height? What was magnitude of rocket's acceleration? Find the height and speed of the rocket after 0.10 seconds after launch.

Problem 2: A lighthouse that rises 49 ft above the surface of the water sits on a rocky cliff that extends 19 feet from its base. A sailor on a boat sights the top of the lighthouse at 30 degrees above the horizontal. If the sailor's eye level is 14 feet above the water, how far is the ship from the rocks?

Please help. Much appreciated!

Homework Equations

The Attempt at a Solution

 

[Yitzach]

Relevant equations are here:
$$\cos\theta=\frac{adjacent}{hypotenuse}$$
$$\sin\theta=\frac{opposite}{hypotenuse}$$
$$\tan\theta=\frac{opposite}{adjacent}$$
$$v_f=v_i+at$$
$$x_f=x_i+.5(v_i+v_f)t$$
$$x_f=x_i+v_it+.5at^2$$
$$v_f^2=v_i^2+2a(x_f-x_i)$$
Move and equate variables as needed. a is a problem specific constant for all equations.

 

[jwang023]

Thank you