Asymmetric initial velocity calculation

[jemerlia]

Homework Statement

A rock is thrown upwards at an angle of 35.0° to the horizontal. The
rock hits a signpost 15.0 m away at a point 2.00 m above the level
from which it was thrown.
Calculate the initial velocity of the rock.

Homework Equations

d = v * t
d= displacement, v=velocity, t=time

x=x0+v0t+1/2gt^2

x= displacement at t
x0 = initial position
v0 = initial velocity
t=time

The Attempt at a Solution

It appears that the x displacement is related:
(1) 15=Vx0 x t

(vx0 is the initial x-component velocity)
because the x velocity is unchanged


The y velocity is related:
(2) 2=vy0t +1/2gt^2

where vy is the initial y vector component

Also:
(3) vx = v0 cos 35
(4) vy = v0 sin 35

It appears possible to substitute for vx, vy so that
15= v0 x cos 35 x t
2= v0 x sin 35 x t + 1/2 gt^2

They look like simultaneous equations but I do not obtain the expected result :(
Help and advice gratefully received.

 

[LowlyPion]

It appears possible to substitute for vx, vy so that
15= v0 x cos 35 x t
2= v0 x sin 35 x t + 1/2 gt^2

Try

15 = V_o*cos35 * t
2 = V_o*sin 35 * t - 1/2 gt²

 

[nlightner]

I would approach this problem by first examining the given information and equations to determine if they are sufficient to solve for the initial velocity of the rock. It seems that the equations provided are correct, and the given information includes the angle at which the rock was thrown, the distance it traveled, and the height at which it hit the signpost.

Next, I would check if the equations are applicable in this scenario. Since the rock is thrown upwards at an angle, we can assume that the initial velocity has both horizontal and vertical components. Therefore, the equations provided are appropriate for this situation.

To solve for the initial velocity, I would use the equations (3) and (4) to substitute for vx and vy in equations (1) and (2). This will give us two equations with two unknowns (v0 and t). We can then solve these equations simultaneously to obtain the values of v0 and t.

It is important to note that the equations provided assume that the acceleration due to gravity (g) is constant and equal to 9.8 m/s^2. If this is not the case, the solution may be slightly different.

In conclusion, the given information and equations are sufficient to solve for the initial velocity of the rock. By substituting for the horizontal and vertical components of velocity, we can solve the simultaneous equations and obtain the desired result.