An arrow is shot at an angle such that it's horizontal velocity is 40 m/s and it's vertical velocity is 20 m/s. Find the horizontal distance the arrow will travel before hitting the ground
To find the horizontal distance the arrow will travel before hitting the ground, we can use the concept of projectile motion.
Projectile motion involves the horizontal and vertical components of motion being independent of each other.
Given that the horizontal velocity (Vx) of the arrow is 40 m/s, and there is no horizontal acceleration in projectile motion, the horizontal distance (d) can be found using the formula:
d = Vx * t
where t is the time taken for the arrow to hit the ground.
To find the time (t), we can look at the vertical motion of the arrow. The vertical motion can be described using the formula:
y = Vyi * t - (1/2) * g * t^2
where y is the vertical displacement (which is zero at the ground level), Vyi is the initial vertical velocity (20 m/s), and g is the acceleration due to gravity (-9.8 m/s^2).
Substituting the known values into the equation, we get:
0 = 20 * t - (1/2) * 9.8 * t^2
Simplifying this equation gives us a quadratic equation:
4.9 * t^2 - 20 * t = 0
We can factor out t and solve for t:
t * (4.9 * t - 20) = 0
This gives us two possible solutions for t:
1) t = 0 (which is the initial time when the arrow was shot)
2) 4.9 * t - 20 = 0
Solving for t in the second equation:
4.9 * t = 20
t = 20 / 4.9
t ≈ 4.08 seconds
Since the initial time (t = 0) is not useful for finding the horizontal distance, we can discard it. Therefore, the arrow will take approximately 4.08 seconds to hit the ground.
Now, use this value of t to calculate the horizontal distance (d):
d = Vx * t
d = 40 * 4.08
d ≈ 163.2 meters
Hence, the horizontal distance the arrow will travel before hitting the ground is approximately 163.2 meters.
do vertical problem first to find time in the air which is twice the time going up
v = Vi - g t
0 at top = 20 - 9.8 t
t = 20/9.8
2 t = time in air = 40/9.8
Now how far horizontal at constant speed of 40?
40(40/9.8) = 1600/9.8
or about 160 meters