A) One strategy in a snowball fight the snowball at a hangover level ground. While your opponent is watching this first snowfall, you throw a second snowball at a low angle and time it to arrive at the same time as the first. Assume both snowballs are the one with the same initial speed 31.3 m/s. The first snow ball is thrown at an angle of 74° above the horizontal. At what angle Sure you throw the second snowball to make ahead the same point as the first? Acceleration of gravity is 9.8 m/s^2. Answer in units of °.
b) How many seconds after the first snowball should be through the second so that they arrive on target at the same time? Answer in units of s.
To solve these questions, we can use the principles of projectile motion.
a) We are given that the initial speed of both snowballs is 31.3 m/s. The first snowball is thrown at an angle of 74° above the horizontal. Let's assume the angle at which the second snowball is thrown is θ.
The horizontal component of the velocity remains constant for both snowballs, so we can equate them:
31.3 * cos(74°) = 31.3 * cos(θ)
Simplifying the equation, we get:
cos(74°) = cos(θ)
Now, we need to find the angle θ that satisfies this equation. We can use an inverse cosine function to solve for θ:
θ = arccos(cos(74°))
θ = 74°
Therefore, the angle at which you should throw the second snowball to hit the same point as the first is also 74°.
b) In order for the second snowball to arrive at the same time as the first, their vertical displacements should be equal. We can use the equations of projectile motion to solve for the time it takes for each snowball to reach the same point.
For the first snowball:
The initial vertical velocity is given by: vy = 31.3 * sin(74°)
The displacement in the vertical direction is: h = 0 (since it starts and ends at the same height)
Using the equation of motion, we can solve for time (t):
h = vy * t + (0.5) * (-9.8) * t^2
0 = (31.3 * sin(74°)) * t + (0.5) * (-9.8) * t^2
For the second snowball:
The initial vertical velocity is given by: vy = 31.3 * sin(θ)
The displacement in the vertical direction is also: h = 0
Using the same equation of motion, we can solve for time (t2):
0 = (31.3 * sin(θ)) * t2 + (0.5) * (-9.8) * t2^2
Since we want the two snowballs to arrive at the same time, t = t2. Therefore, we can set the equations equal to each other:
(31.3 * sin(74°)) * t = (31.3 * sin(θ)) * t2
Simplifying, we get:
sin(74°) = sin(θ)
Now, we can solve for the angle θ using an inverse sine function:
θ = arcsin(sin(74°))
θ = 74°
Therefore, both snowballs should be thrown at the same angle of 74° and they will arrive at the same time.