We have a projectile launched upward with an initial horizontal velocity of

20 m/s and an initial vertical velocity of 30 m/s.
1. What is the actual initial speed of the projectile?
2. What happens to the horizontal component of the velocity as the projectile flies through
the air?
3. What happens to the vertical component of the projectile as it flies through the air?
4. At the projectile’s maximum height, what is the horizontal component of its velocity?
5. At the projectile’s maximum height, what is the vertical component of its velocity?

1) sqrt (20^2 + 30^2)

2) no horizontal force so no change in horizontal speed

3) slows to zero at top then comes back to original speed but downward

4) Like we said in #2, it is the same until it hits the charging warthog.

5) it is at max height, no speed up any more and no speed down yet.

Hey - you do not need me for this !

1. To find the actual initial speed of the projectile, we can use the Pythagorean theorem. The initial speed (or magnitude of the velocity) is given by:

Initial speed = √(horizontal velocity^2 + vertical velocity^2)

Plugging in the values, we get:

Initial speed = √(20 m/s)^2 + (30 m/s)^2)
= √(400 + 900)
= √1300
≈ 36.06 m/s

Therefore, the actual initial speed of the projectile is approximately 36.06 m/s.

2. The horizontal component of the velocity remains constant throughout the motion of the projectile. It doesn't change as the projectile flies through the air. In this case, the initial horizontal velocity of 20 m/s will remain the same during the entire flight.

3. The vertical component of the projectile's velocity changes continuously due to the effect of gravity. As the projectile moves upward, the vertical velocity decreases until it reaches its maximum height. At the peak of its trajectory, the vertical velocity becomes zero since the object momentarily comes to a halt. Afterward, as the projectile comes back down, the vertical velocity increases in magnitude, but in the opposite direction. Gravity causes the projectile to accelerate downward, increasing the vertical velocity.

4. At the projectile's maximum height, the horizontal component of its velocity remains unchanged. Therefore, the horizontal component of the velocity will still be 20 m/s.

5. At the projectile's maximum height, the vertical component of its velocity is zero. The projectile briefly stops moving vertically at the top of its trajectory before descending. Hence, the vertical component of the velocity is zero at the maximum height.

To answer these questions, we first need to understand the principles of projectile motion.

When a projectile is launched, it follows a curved path known as a parabola. The two main components of the projectile's motion are the horizontal motion and the vertical motion.

1. To find the actual initial speed of the projectile, we need to calculate its total initial velocity. This can be done using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the horizontal and vertical components of the velocity form a right triangle.

Therefore, we can calculate the initial speed as follows:
Initial speed = √(horizontal velocity^2 + vertical velocity^2)
In this case, the horizontal velocity is 20 m/s and the vertical velocity is 30 m/s.
So, the initial speed = √(20^2 + 30^2) = √(400 + 900) = √1300 ≈ 36.06 m/s.

2. As the projectile flies through the air, the horizontal component of its velocity remains constant. This is because there are no horizontal forces acting on the projectile (assuming no air resistance), so it will continue to move with a constant horizontal velocity.

3. The vertical component of the projectile's velocity changes due to the influence of gravity. Gravity pulls the projectile downward, causing it to accelerate in the vertical direction. As a result, the vertical velocity of the projectile decreases until it reaches its maximum height, where it momentarily becomes zero. After reaching the maximum height, the vertical velocity continues to decrease and then becomes negative as the projectile starts to fall back down.

4. At the projectile’s maximum height, its horizontal velocity remains the same as the initial horizontal velocity. This is because, as mentioned earlier, the horizontal component of the velocity remains constant throughout the projectile's motion.

5. At the projectile’s maximum height, the vertical component of its velocity is zero. This is because at the highest point of the projectile's trajectory, its vertical velocity reaches a maximum value of zero before it starts to decrease due to the downward pull of gravity.