Asymmetric initial velocity calculation

In summary, the problem involves calculating the initial velocity of a rock thrown at an angle of 35.0° to the horizontal, which hits a signpost 15.0 m away and 2.00 m above the starting point. The equations used are d = v * t and x = x0 + v0t + 1/2gt^2, with the initial x and y velocities represented by vx0 and vy0. Substituting these values and solving for Vo results in a system of simultaneous equations, which can be solved to find the initial velocity.
  • #1
jemerlia
28
0

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.
 
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  • #2
jemerlia said:
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 = Vo*cos35 * t
2 = Vo*sin 35 * t - 1/2 gt2
 
  • #3


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.
 

Related to Asymmetric initial velocity calculation

1. How is the initial velocity calculated for an asymmetric object?

The initial velocity of an asymmetric object is calculated by taking into account the individual velocities of each component of the object. This includes the magnitude and direction of the velocity of each component. The combined velocity is then calculated using vector addition.

2. What factors are considered when calculating the initial velocity of an asymmetric object?

The factors that are considered when calculating the initial velocity of an asymmetric object include the mass, shape, and velocity of each individual component, as well as any external forces acting on the object.

3. How is the velocity of each component of an asymmetric object determined?

The velocity of each component of an asymmetric object is determined through experiments or simulations. This involves measuring the velocity of each component separately and taking into account any external factors that may impact the velocity, such as air resistance or friction.

4. Can the initial velocity of an asymmetric object change over time?

Yes, the initial velocity of an asymmetric object can change over time due to external forces acting on the object or changes in the individual velocities of each component. This is why it is important to continuously monitor and recalculate the initial velocity as needed.

5. How is the initial velocity of an asymmetric object used in scientific research?

The initial velocity of an asymmetric object is a crucial factor in understanding and predicting the motion of the object. It is used in various fields of science, such as physics, engineering, and biomechanics, to study and analyze the behavior of asymmetric objects in motion.

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