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1. One morning, while little Lenlen’s mother was busy in the kitchen, Little Lenlen rolls off the bed that is 0.50 m above the floor. If the floor is hardwood, little Lenlen’s head is brought to rest in approx. 2.0 mm. If the floor is carpeted, this stopping distance is increased to about 1.0 cm. Calculate the magnitude and duration of the acceleration in both cases, to determine the risk of injury. Assume that little Lenlen remains horizontal during the fall to the floor. (Note: A more complicated fall could result in a head velocity greater or less than the speed you calculate. Traumatic brain injury such as concussion results when the head undergoes a very large acceleration. Generally, an acceleration less than 800 m/s2 lasting for any length of time will not cause injury, whereas an acceleration greater than 1000m/s2 lasting for at least 1 ms will cause injury.)
2. A summersault swimmer stands on a high platform jumps vertically upward with a velocity of magnitude 2.5 m/s. Air resistance maybe ignored.
a.) At what time after moving from the platform does the swimmer have a velocity of 0.25 m/s upward?
b.) At what time does she has a velocity of 0.25 m/s downward?
c.) When is the displacement of the swimmer from its initial position zero?
d.) When is the velocity of the swimmer zero?
e.) What are the magnitude and direction of the acceleration while the swimmer is
i.) Moving upward?
ii.) Moving downward?
A stone is projected in a vertical plane from the ground with a velocity of 5 m/s. at an elevation of 60°. With what velocity, must another stone be projected at an angle of 45° in order to have the same horizontal range? Given g = 10 m/s^2
What is the strength of the ionic interactions between an ion with 2 positive charges and an ion with 1 negative charges, when the distance between them is 15.5 nanometers and the solvent is benzene, with a dielectric constant of 4.6?
A kicked football leaves the ground at an angle θ = 38.8° with a velocity of 22.1 m/s. a) Calculate the maximum height (m). b) the time of travel before the football hits the ground (s). c) how far away it hits the ground (m). Assume the ball leaves the foot at ground level, and ignore air resistance and rotation of the ball.
According to the Guinness Book of World Records, the longest home run ever measured was hit by Roy "Dizzy"Carlyle in a minor league game. The ball traveled 196.4 meters before landing on the ground outside the ballpark. Assuming the ball's initial velocity was in a direction 45° above the horizontal and ignoring air resistance, what did the initial speed of the ball,in meters per second, need to be to produce such a home run if the ball was hit at a point 0.7 m above the ground level? How far would the ball be above a fence 3.0 meters high if the fence was 98 meters from the home plate? Write your answer in meters.
The rear wheel of a 150 kg tricycle accidentally ran over a nail. The circular tip of the nail has a diameter of 0.001 m. How much pressure did the wheel of the tricycle experience assuming that the entire weight of the tricycle is concentrated on the rear wheel that ran over the nail.
Given two vectors A=6i + 3j - k and B = 4i -5j + 8k , find the magnitude of the vector 2A - 3B.
The electromagnetic spectrum contains various types of radiation with different properties. The James Webb Space Telescope is not like an optical telescope at home and does not capture visible light; instead, it observes the sky in the infrared spectrum.
Explain what infrared radiation is and answer the following questions: How is infrared radiation different from visible light? Why does the JWST observe infrared light, and what are the scientific advantages for astronomers?
The electromagnetic spectrum contains various types of radiation with different properties. The James Webb Space Telescope is not like an optical telescope at home and does not capture visible light; instead, it observes the sky in the infrared spectrum.
Explain what infrared radiation is and answer the following questions: How is infrared radiation different from visible light? Why does the JWST observe infrared light, and what are the scientific advantages for astronomers?
