Question

What time is required to travel a distance of 330 km along a freeway at the following constant speeds? -(a) 53.5 km/h -(b) 57.0 km/h

Compute the average speed in m/s of a runner who completes a mile in 3.88 min?

A force directed 54.1° below the positive x-axis has an x component of 5.02 lb. Find its y component.

A certain vector A, of magnitude 5.49 units, points in a direction 31.0° to the left of the negative y-axis. Find Ax and Ay. At t = 0 the coordinates of a particle are x = 0, y = 2.20 m.

At a time 1.11 s later, its coordinates are x = 2.91 m, y = 3.80 m. Find the components of the particle's average velocity during this time interval

Find the resultant of the vectors shown in the figure below. (Take a = 18.4°, b = 64.8° and c = 27.9°.) magnitude___Units direction____counterclockwise from the positive x-axis

A traveler first drives 18.8 km east, then 32.7 km southeast, and finally 10.6 km south. Find the traveler's total displacement. magnitude_____ direction____south of east

During a 9.8 s interval, the position of a particle changes from x = 2.04 m, y = 3.68 m to x = 6.42 m, y = 3.68 m. Find the particle's average velocity. Magnitude_____ Direction________

Find the resultant of the vectors shown in the figure below. (Take a = 18.4°, b = 64.8° and c = 27.9°.) magnitude______Units    Direction________ counterclockwise from the positive x-axis

Answer 1

1. What time is required to travel a distance of 330 km along a freeway at the following constant speeds? -(a) 53.5 km/h -(b) 57.0 km/h

a) V = S/t

t = S/v

t = 330/53.5 = 6.17 hours

b) V = S/t

t = S/v

t = 330/57 = 5.79 hours

2. Compute the average speed in m/s of a runner who completes a mile in 3.88 min?

V = S/t = 1 mile / 3.88 min

V = 1 x 1609.344 meters / 3.88 x 60 seconds

V = 6.91 m/s

3. A force directed 54.1° below the positive x-axis has an x component of 5.02 lb. Find its y component.

F_x = 5.02 lb

F_x = Fcos54.1 = 5.02

F = 5.02/cos54.1

F_y = Fsin54.1

F_y = 5.02sin54.1/cos54.1

F_y = 5.02tan54.1 = 6.93 lb in the negative y axis

4. A certain vector A, of magnitude 5.49 units, points in a direction 31.0° to the left of the negative y-axis. Find Ax and Ay.

F = 5.49

F_x = Fsin31.0 ( not Fcos31.0 in this case)

F_x = 2.83 units in negative x axis

F_y = Fcos31.0

F_y = 4.71 units in negative y axis

5. At t = 0 the coordinates of a particle are x = 0, y = 2.20 m. At a time 1.11 s later, its coordinates are x = 2.91 m, y = 3.80 m. Find the components of the particle's average velocity during this time interval

V_x = Δx / Δt = (2.91 - 0) / 1.11 = 2.62 m/s

V_y = Δy / Δt = (3.80-2.20) / 1.11 = 1.44 m/s

6. A traveler first drives 18.8 km east, then 32.7 km southeast, and finally 10.6 km south. Find the traveler's total displacement. magnitude_____ direction____south of east

Thee are three displacements

The total displacement in x axis

Δx = 18.8 + 32.7cos45 + 0 = 41.9 km

The total displacement in y axis

Δy = 0 + 32.7sin45 + 10.6 = 33.7 km

Total displacement

S = √(Δx²+Δy²)

S = √(41.9² + 33.7²)

S = 53.8 km

Φ = tan^-1(Δy/Δx)

Φ = 88.3^o south of east

7. During a 9.8 s interval, the position of a particle changes from x = 2.04 m, y = 3.68 m to x = 6.42 m, y = 3.68 m. Find the particle's average velocity. Magnitude_____ Direction________

V_x = 6.2-2.04 / 9.8 = 0.447 m/s

V_y = 3.68-3.68 / 9.8 = 0 m/s

V = √(v_x²+ v_y²) = 0.447 m/s