Practice 3B: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | Go up
Resolving vectors

1. How fast must a truck travel to stay beneath an airplane that is moving 105 km/h at an angle of 25 deg to the ground?

Here's what you know, va = 105 km/h, and q = 25 deg. Use the formula cos q= vx / va and plug in: cos (25 deg) = vx / 105 km/h, so vx = (105 km/h)(cos (25 deg)) = 95.1623176388 km/h = 95 km/h

2. What is the magnitude of the vertical component of the velocity of the plane in item 1?

Here's what you know, va = 105 km/h, and q = 25 deg. Use the formula sin q= vy / va and plug in: sin (25 deg) = vy / 105 km/h, so vy = (105 km/h)(sin (25 deg)) = 44.3749174828 km/h = 44 km/h

3. A truck drives up a hill with a 15 deg incline. If the truck has a constant speed of 22m/s, what are the horizontal and vertical components of the truck's velocity?

Here's what you know, vt = 22 m/s, and q = 15 deg. Use the formula cos q= vx / vt and plug in: cos (15 deg) = vx / 22 m/s, so vx = (22 m/s)(cos (15 deg)) = 21.2503681784 m/s = 21 m/s. Use the formula sin q = vy / vt and plug in: sin (15 deg) = vy / 22 m/s, so vy = (22 m/s)(sin (15 deg)) = 5.69401899226 m/s = 5.7 m/s. Yielding vx = 22 m/s and vy = 5.7 m/s.

4. What are the horizontal and vertical components of a cat's displacement when it has climbed 5 m directly up a tree?

Since the tree is directly vertical the entire magnitude of 5 m is the vertical component leaving 0 m for the horizontal component.

5. Find the horizontal and vertical components of the 125 m displacement of a superhero who flies down the top of a tall building at an angle of 25 deg below the horizontal?

Here's what you know, d = 125 m, and q = -25 deg (it's negative 'cause it's below the horizontal). Use the formula cos q= Dx / d and plug in: cos (-25 deg) = Dx / 125 m, so Dx = (125 m)(cos (-25 deg)) = 113.28847338 m = 110 m. Use the formula sin q= Dy / d and plug in: sin (-25 deg) = Dy / 125 m, so Dy = (125 m)(sin (-25 deg)) = -52.8272827176 m = -53 m. Yielding 110 m horizontal and -53 m vertical.