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

[sehar100]

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

 

[berkeman]

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[m2003]

1. Balloon:

To solve this problem, we can use the equation of motion for vertical motion: d = vit + 1/2at^2, where d is the displacement, vi is the initial velocity, a is the acceleration, and t is the time.

In this case, the displacement is 50 meters (since the balloon starts at 50 meters above the ground and needs to reach the ground), the initial velocity is 15 meters/sec (since the wind is blowing the balloon at this speed), and the acceleration is -9.8 m/s^2 (since the balloon is accelerating downwards due to gravity). We can also assume that the final displacement is 0 (since the balloon needs to reach the ground).

Plugging in these values, we get the following equation: 0 = 50 + 15t - 4.9t^2

Solving for t, we get t = 4.44 seconds. This is the amount of time the balloonist needs to wait before dropping the ribbon in order for it to hit the target.

2. Ball:

(a) To find the initial vertical component of the velocity, we can use the equation of motion for vertical motion: d = vit + 1/2at^2, where d is the displacement, vi is the initial velocity, a is the acceleration, and t is the time.

In this case, the displacement is 3.4 meters (since this is the maximum height of the ball's trajectory), the initial velocity is unknown (represented by vi), the acceleration is -9.8 m/s^2 (since the ball is accelerating downwards due to gravity), and the time is unknown (represented by t).

Plugging in these values, we get the following equation: 3.4 = vi(t) - 4.9t^2

Since we have two unknowns, we cannot solve for vi. However, we can use the information given in part (b) and (c) to find the initial velocity.

(b) To find the time for the ball to reach maximum height, we can use the equation of motion for vertical motion: d = vit + 1/2at^2, where d is the displacement, vi is the initial velocity, a is the acceleration, and t is the time.

In this case, the displacement is 3.4 meters (since this is the maximum height of the ball's trajectory), the