1)The traffic light turns green, and the driver of a high-performance car slams the accelerator to the floor. The accelerometer registers 29.0 m/s2. Convert this reading to km/min2.
2)Convert 4.45 103 kg/m3 to g/cm3.
3)While standing atop a building 53.6 m tall, you spot a friend standing on a street corner. Using a protractor and a dangling plumb bob, you find that the angle between the horizontal and the direction to the spot on the sidewalk where your friend is standing is 25.8°. Your eyes are located 1.79 m above the top of the building. How far away from the foot of the building is your friend?
4)The eye of a hurricane passes over Grand Bahama Island in a direction 60.0° north of west with a speed of 39.0 km/h. Three hours later, the course of the hurricane suddenly shifts due north, and its speed slows to 22.0 km/h. How far from Grand Bahama is the hurricane 4.70 h after it passes over the island?
Please explain each problem step by step and individually with the answers. Thanks
1) To convert m/s^2 to km/min^2, we need to convert meters to kilometers and seconds to minutes.
Given:
Acceleration (a) = 29.0 m/s^2
Step 1: Convert meters to kilometers
1 kilometer (km) is equal to 1000 meters (m). Therefore, to convert from meters to kilometers, we divide the value by 1000.
Acceleration (a) in km/s^2 = 29.0 m/s^2 / 1000 = 0.029 km/s^2
Step 2: Convert seconds to minutes
1 minute (min) is equal to 60 seconds (s). Therefore, to convert from seconds to minutes, we divide the value by 60.
Acceleration (a) in km/min^2 = 0.029 km/s^2 * (1 min / 60 s) = 0.0004833 km/min^2
The acceleration of 29.0 m/s^2 is equivalent to 0.0004833 km/min^2.
2) To convert kg/m^3 to g/cm^3, we need to convert kilograms to grams and meters to centimeters.
Given:
Density (ρ) = 4.45 * 10^3 kg/m^3
Step 1: Convert kilograms to grams
1 kilogram (kg) is equal to 1000 grams (g). Therefore, to convert from kilograms to grams, we multiply the value by 1000.
Density (ρ) in g/m^3 = 4.45 * 10^3 kg/m^3 * 1000 = 4.45 * 10^6 g/m^3
Step 2: Convert meters to centimeters
1 meter (m) is equal to 100 centimeters (cm). Therefore, to convert from meters to centimeters, we multiply the value by 100.
Density (ρ) in g/cm^3 = 4.45 * 10^6 g/m^3 * (1 cm / 100 m)^3 = 4.45 g/cm^3
The density of 4.45 * 10^3 kg/m^3 is equivalent to 4.45 g/cm^3.
3) To find the distance between you and your friend, we can use trigonometry.
Given:
Height of building (h) = 53.6 m
Angle between horizontal and direction to friend (θ) = 25.8°
Height of eyes (H) = 1.79 m
Step 1: Calculate the total height from eyes to friend
Total height (H_total) = Height of building (h) + Height of eyes (H)
H_total = 53.6 m + 1.79 m = 55.39 m
Step 2: Calculate the horizontal distance to the friend using trigonometry
The horizontal distance (d) can be calculated using the formula:
d = H_total / tan(θ)
Let's convert the angle to radians first:
θ_radians = θ * (π/180) = 25.8° * (π/180) = 0.45 rad
Now, substitute the values into the formula:
d = 55.39 m / tan(0.45 rad) = 55.39 m / 0.995 = 55.60 m
The friend is approximately 55.60 meters away from the foot of the building.
4) To find the distance of the hurricane from Grand Bahama Island after 4.70 hours, we need to calculate the displacement using the initial velocity, time, and change in velocity.
Given:
Initial velocity (v1) = 39.0 km/h
Change in velocity (Δv) = 22.0 km/h
Time (t) = 4.70 h
Angle (θ) = 60.0°
Step 1: Calculate the initial velocity components in the x and y directions
v1x = v1 * cos(θ)
v1y = v1 * sin(θ)
v1x = 39.0 km/h * cos(60.0°) = 19.5 km/h
v1y = 39.0 km/h * sin(60.0°) = 33.8 km/h
Step 2: Calculate the displacement in the x direction
Displacement (dx) = v1x * t + (1/2) * Δv * t
dx = (19.5 km/h * 4.70 h) + (1/2) * (22.0 km/h) * (4.70 h) = 91.65 km + 51.87 km = 143.52 km
Step 3: Calculate the displacement in the y direction
Displacement (dy) = v1y * t
dy = 33.8 km/h * 4.70 h = 158.86 km
Step 4: Calculate the magnitude of the displacement
Magnitude of displacement (d) = √(dx^2 + dy^2)
d = √(143.52 km^2 + 158.86 km^2) = √(20584.12 km^2) = 143.49 km
After 4.70 hours, the hurricane is approximately 143.49 kilometers away from Grand Bahama Island.