The target is to be dropped from the point
A at t = 0, the same moment as the gun is
fired. The bullet hits the target at a point
P. Let the initial speed of the bullet be v0 =
106 m/s, let the angle between the vector v0
and the horizontal (x) direction be θ = 57.3
and let AB = 91 m. The distance d = OB is
the x-coordinate of the target.
The acceleration of gravity is 9.8 m/s^2
The height BP where the collision takes
place is
i know i have to find the x component and y component in this equation
To find the height BP where the collision takes place, we need to calculate the vertical displacement of the bullet from the time it is fired until it hits the target.
Given:
Initial speed of the bullet, v0 = 106 m/s
Angle between the vector v0 and the horizontal direction, θ = 57.3°
Acceleration due to gravity, g = 9.8 m/s^2
Distance AB = 91 m
First, we need to resolve the initial velocity of the bullet into its horizontal and vertical components.
The horizontal component of the initial velocity (v0x) can be found using the formula:
v0x = v0 * cos(θ)
Substituting the given values:
v0x = 106 m/s * cos(57.3°)
The vertical component of the initial velocity (v0y) can be found using the formula:
v0y = v0 * sin(θ)
Substituting the given values:
v0y = 106 m/s * sin(57.3°)
Next, we can use the kinematic equation for vertical motion to find the time taken by the bullet to reach the target.
The equation is:
d = v0y * t + (1/2) * g * t^2
where d is the vertical displacement (which is the height BP), v0y is the vertical component of the initial velocity, g is the acceleration due to gravity, and t is the time taken.
Since the bullet is dropped from the same height as the gun is fired, the vertical displacement d is equal to zero.
Substituting the values:
0 = (106 m/s * sin(57.3°)) * t + (1/2) * (9.8 m/s^2) * t^2
Simplifying the equation:
(4.9 m/s^2) * t^2 + (106 m/s * sin(57.3°)) * t = 0
Solving this quadratic equation will give us two solutions: t = 0 (initial time) and t = t_collision (time when the bullet hits the target).
We can ignore the first solution t = 0, and solve for t_collision by finding the positive root of the equation.
Once we have the value of t_collision, we can substitute it back into the kinematic equation to find the height BP.
I hope this explanation helps you understand how to find the height BP where the collision takes place!