1. The summit of a mountain, 2088 m above base camp, is measured on a map to be 4578 m horizontally from the camp in a direction 32.4° west of north. Choose the x axis east, y axis north, and z axis up. What are the components of the displacement vector from camp to summit?
X= ?
Y=?
Z=?
What is the magnitude?
2. An athlete executing a long jump leaves the ground at a 35° angle and travels 8.30 m.
I figured out the takeoff speed was 9.31 m/s
If this speed were increased by just 3.0%, how much longer would the jump be?
X= ?
Y=?
Z=?
What is the magnitude?
2. An athlete executing a long jump leaves the ground at a 35° angle and travels 8.30 m.
I figured out the takeoff speed was 9.31 m/s
If this speed were increased by just 3.0%, how much longer would the jump be?
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1. The summit of a mountain, 2088 m above base camp, is measured on a map to be 4578 m horizontally from the camp in a direction 32.4° west of north. Choose the x axis east, y axis north, and z axis up. What are the components of the displacement vector from camp to summit?
The height is z component.
32.4° west of north means the west component = 4578 * sin 32.4°, and the north component = 4578 * cos 32.4°
Positive x axis is east, so west is negative x
X= -4578 * sin 32.4°,
Y= +4578 * cos 32.4°
Z= 2088
Magnitude = square root of the sum of the squares = [(-4578 * sin 32.4°)^2 + (+4578 * cos 32.4°)^2 + 2088^2]^0.5
2. An athlete executing a long jump leaves the ground at a 35° angle and travels 8.30 m.
Use the Range equation
Range = v^2/g * sin 2 θ
8.30 = v^2/9.8 * sin 70°
v = [(8.30 * 9.8) ÷ sin 70°]^0.5 = 9.30 m/s
Range = v^2/g * sin 2 θ
Increase of 3% means multiply by 1.03
v = 1.03 * 9.30
Range = (1.03 * 9.30)^2/9.8 * sin 70° = 8.8 m
The height is z component.
32.4° west of north means the west component = 4578 * sin 32.4°, and the north component = 4578 * cos 32.4°
Positive x axis is east, so west is negative x
X= -4578 * sin 32.4°,
Y= +4578 * cos 32.4°
Z= 2088
Magnitude = square root of the sum of the squares = [(-4578 * sin 32.4°)^2 + (+4578 * cos 32.4°)^2 + 2088^2]^0.5
2. An athlete executing a long jump leaves the ground at a 35° angle and travels 8.30 m.
Use the Range equation
Range = v^2/g * sin 2 θ
8.30 = v^2/9.8 * sin 70°
v = [(8.30 * 9.8) ÷ sin 70°]^0.5 = 9.30 m/s
Range = v^2/g * sin 2 θ
Increase of 3% means multiply by 1.03
v = 1.03 * 9.30
Range = (1.03 * 9.30)^2/9.8 * sin 70° = 8.8 m