Physics (Newton's 2nd Law, Constant Acceleration, Vectors)?

A block is projected up a frictionless inclined plane with initial speed Vo = 3.42 m/s. The angle of incline is = 32.1°.





(a) How far up the plane does the block go?


_________ m


(b) How long does it take to get there?


_________ s


(c) What is its speed when it gets back to the bottom?


_________ m/s





I tried, but didn't reach the right result.

Physics (Newton's 2nd Law, Constant Acceleration, Vectors)?
Easy peasy :)





Firstly, you need to translate the vector of initial movement into its two axis, one going up and down, the same direction as gravity is going, and the other side-to-side.





This can be done using trigonometry. The speed in up/down can be determined using a triangle with hypotenuse being 3.42m/s and the incline angle of 32.1 degrees. sin(32.1) = y/3.42. Y = 1.82m/s. Then, determine the side to side componant with Pythagorean Theorem: 3.42^2 = X^2 + 1.82^2. X = 2.9m/s





Now that you have that figured out, you can determine the amount of time it takes for the object to accelerate to 0m/s (from Y=1.82m/s) using the At + Vo = V(t) formula. Given that gravity is 9.81m/s/s we have:


-9.81m/s/s * t = -1.82m/s


-9.81m/s/s * t = -1.82m/s


t = 0.185 seconds (b)





You can determine (a) by using the At^2 + Vt + Xo = X(t) formula by plugging in t = 0.185 seconds.


-9.81m/s/s * t^2 + 1.82m/s * t = X(t)


-9.81m/s/s * (0.185)^2 + 1.82m/s * 0.185 = X(t)


-0.3357m + 0.3367m = X(t) = 0.001m ( 1mm )





The speed when it comes back down can be determined by seeing how long it falls from its highest point (1mm) and then adding in a side-ways componant.


At^2 + Vt + 1mm = X(t)


At^2 + Vt = -0.001m


-9.81m/s/s * t^2 = 0.001m


t^2 = 0.0001


t = 0.01s (this means the object falls for 0.01 seconds before being at the starting position/bottom)





At = Vy... -9.81m/s/s * 0.01 = -0.1m/s





Plugging this value back into the original starting triangle, putting it at the up and down spot, we can see see that:


sin(32.1) = -0.1 / X


X = 0.188m/s (c)





Hopefully my math isnt wrong. :)