Stone thrown from cliff at 53°: finding time, height, range, and final velocity

[MissJewels]

Homework Statement

A stone is thrown from a cliff 100 meters high with an initial velocity v₀ = 25 m / s and at an angle of 53° projection from the horizontal axis. determine:
a) the time before it reaches the ground
b) the maximum height
c) its horizontal reach
d) its speed when it hits the ground

Homework Equations

I selected these:
v_x0 = v₀cos(53)
v_y0 = v₀sin(53)

Then I applied these t the following equations:
x_f= v_x0t
y_f= y₀ + v_y0t+ (1/2)(-9,8)t²

t= ( -b± √(b² - 4ac) ) / 2a

The Attempt at a Solution

So, for part a), using the above equations I found:

v_x0 = v₀cos(53)
v_x0 = 25cos(53) = -22,96
x_f= v_x0t
x_f= -22,96t

v_y0 = v₀sin(53)
v_y0 = 25sin(53) = 9,898
y_f= y₀ + v_y0t+ (1/2)(-9,8)t²
0= 100 + 9,898t+ (1/2)(-9,8)t²

Then, with that last equation, I used this equation: t= ( -b± √(b² - 4ac) ) / 2a

to find t= -3,62s
When the answer SHOULD BE 7s... What am i doing wrong?


then, i tried b) using v_f= 0
using the equation(H is maxheight):

v_f² = v₀ -2(9,8)(H-100)
0 = 25² -16,9H +1690
H = 136,98 m
And the right answer should be 120m... GRR !

As for c), I don'T quite understand how to measure it... do i find x_f?

d) Its supposed to be (15i -48,6j) m/s but i forgot how to calculate vectors.


ANYWAY PLEASE HELP! Its easy for you, but for me, this is hard. ;(

 

[iRaid]

These equations usually make problems much easier:

$x(t) = v_{o}cos\theta$

$y(t) = v_{o}sin\theta - \frac{1}{2}gt^{2} + h$

v_o: Initial velocity
h: height

 

[gneill]

Quadratic equations have two roots. Sometimes only one of them will make physical sense for a given situation.

EDIT: Also, make sure that your calculator is set for DEGREES rather than RADIANS if your angles are given in degrees!

 

[MissJewels]

Thanks for the replies, but i was wondering if someone could perhaps check my work? Tell me what I am doing wrong, if i miscalculated? I'm still in a nut.
Also, I have tried finding the two roots for the quadratic equation, and neither give me the proper answer.

 

[SteamKing]

Well, you could show us your calculations after you have fixed the known errors.

 

[MissJewels]

I got it! I've been repeating the same silly mistake over and over again.