Solve Hot Air Balloon & Ball Throwing Problems: Help Needed Urgently

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A hot air balloonist needs to determine the optimal time to drop a ribbon from a height of 50 meters, 100 meters from a target, factoring in a wind speed of 15 meters/sec. The discussion also includes a problem involving a ball thrown to a roof 15 meters high, requiring calculations for the initial vertical velocity, time to maximum height, and time to fall to the rooftop. Additionally, there is a scenario where a ball is thrown at 30 m/s at a 45° angle from an 11-meter height, with questions about time of flight, maximum height, landing distance, and impact speed. Participants are required to show their work for these problems to receive tutorial assistance. Clear problem-solving steps are essential for effective help in these physics challenges.
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1. Balloon

A hot air balloon competition requires a balloonist to drop a ribbon onto a target on the ground. Initially the hot air balloon is 50 meters above the ground and 100 meters from the target. The wind is blowing the balloon at v = 15 meters/sec on a course to travel directly over the target. The ribbon is heavy enough that any effects of the air slowing the vertical velocity of the ribbon are negligible. How long should the balloonist wait to drop the ribbon so that it will hit the target?

time =?

2. A ball is thrown from the ground onto a roof of height 15 m from a distance of 7 meters away as shown in the diagram. The maximum height of the ball's trajectory is 3.4 meters above the top of the roof.

(a) Find the required initial vertical component of the velocity, Vy.

Vy = ?? m/s

(b) Find the time for the ball to reach maximum height.

t = ?? s

(c) Find the time for the ball to fall from the maximum height to the rooftop.

t = ?? s

(d) Find the initial horizontal component of the velocity.

vx = ?? m/s

3. A ball is thrown with an initial speed of 30 m/s at an angle of 45°.The ball is thrown from a height of 11 m and lands on the ground.

(a) Find the time of flight.
t = ?? s

(b) Find the maximum height.
h = ?? m

(c) Find the distance from where the ball is thrown to where it lands.
d = ?? m

(d) Find the speed at the impact.
v = ?? m/s
 
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