a hot air balloon is rising vertically 10 ft/sec while the wind is blowing horizontally 5ft/sec. Find the speed of the balloon and the angle x that it makes with the horizontal.

I know that the speed of the balloon is
the square root of (10)^2 + (5)^2, but I was wondering if someone could tell me why the speed is equal to that. Thanks.

1. 👍
2. 👎
3. 👁
1. from the origin draw a vertical line of length 10
from the origin draw a horizontal line of length 5

Complete the rectangle, and draw in the diagonal.
That diagonal is the resultant velocity.
You now have a right-angled triangle with base of 5 and height of 10
let the hypotenuse be h
h^2 = 10^2+5^2 = 125
h = √125 = 5√5 = appr. 11.18
to find the angle
sinx = 10/11.18
x = 63.4°
we could have done : tanx = 10/5 = 2
x = 63.4°

1. 👍
2. 👎
2. You can draw a triangle for velocity, even though usually you do it for distances, because the distance is velocity * time. The time elapsed is just a scale factor, so the velocity triangle is just the distance triangle, scaled by how much time has elapsed.

1. 👍
2. 👎

## Similar Questions

1. ### physics

A hot-air balloon is rising upward with a constant speed of 2.50 m/s. When the balloon is 3.00 m above the ground, the balloonist accidentally drops a compass over the side of the balloon. How much time elapses before the compass

2. ### Physics

A hot-air balloonist, rising vertically with a constant speed of 5.00 m/s releases a sandbag at the instant the balloon is 40.0 m above the ground. After it is released, the sandbag encounters no appreciable air drag. Compute the

3. ### Physics

Hot air balloons float in the air because of the difference in density between cold and hot air. In this problem, you will estimate the minimum temperature the gas inside the balloon needs to be, for it to take off. To do this,

4. ### Physics

A hot-air balloon is rising upward with a constant speed of 2.21 m/s. When the balloon is 2.25 m above the ground, the balloonist accidentally drops a compass over the side of the balloon. How much time elapses before the compass

1. ### Calculus

A balloon is rising vertically above a level, straight road at a constant rate of 1 foot/second. Just when the balloon is 65 feet above the ground, a bicycle passes under it going 17 feet/sec. How fast is the distance between the

2. ### Physics

A hot-air balloon is rising vertically at a speed of 10 m s–1. An object is released from the balloon. The graph shows how the velocity of the object varies with time from when it leaves the balloon to when it reaches the ground

3. ### Physics

A hot-air balloon is rising upwards at a constant velocity of 5m.s . When the balloon is 100m above the ground , a sandbag is dropped from it. Will the velocity of the hot-air balloon increase , decrease or remain the same

4. ### Physics

A hot-air balloon is accelerating upward under the influence of two forces, its weight and the buoyant force. For simplicity, consider the weight to be only that of the hot air within the balloon, thus ignoring the balloon fabric

1. ### Physics

On a perfect fall day, you are hovering at a low altitude in a hot-air balloon, accelerated neither upward nor downward. The total weight of the balloon, including its load and the hot air in it, is 12000 N. What is the volume of

2. ### Calculus

A balloon is rising at a constant speed of 5 ft/sec. A boy is cycling along a straight road at a constant speed of 15 ft/sec. When he passes under the balloon, it is 5 feet above him. Determine how fast the distance between the

3. ### physics

A hot-air balloon is rising upward with a constant speed of 3.06 m/s. When the balloon is 9.31 m above the ground, the balloonist accidentally drops a compass over the side of the balloon. How much time elapses before the compass

4. ### calculus

When a ball is thrown vertically upward into the air with a velocity of 79 ft/sec its height, y(t), in feet after t seconds is given by y(t) = 79t − 16t 2 . Find the average velocity of the ball over the interval from 3 to 3 + h