The acceleration of a rocket travelling upward is given by: a = (6+ 0.02s), where s is in meters. Determine the velocity needed for the rocket to reach an altitude of s=100m from rest.
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- The acceleration of an object (in m/s2) is given by the function a(t)=7sin(t)a(t)=7sin(t). The initial velocity of the object is v(0)=−1v(0)=-1 m/s. Round your answers to four decimal places. v(t) = -7cos(t) + 6 The objects displacement from time 0 to 3 is: 17.01216 meters Find the total distance traveled by the object from time 0 to time 3.answer in Three significant digitsWhat is the velocity of a car that travels from mile marker 32 on I-10 to mile marker 312 on I-10 in a time of 2 hours and 45 minutes?
- Nerve impulses in a human body travel at a speed of about 100 m/s. Suppose a person accidentally steps barefoot on a pebble. About how much time does it take the nerve impulse to travel from the foot to the brain (in s)? Assume the person is 1.60 m tall and the nerve impulse travels at uniform speed.A cart is propelled over an its greatest y coordinate? xy plane with acceleration components a, = 6.8 m/s? and a, = -1.5 m/s2. Its initial velocity has components Vox = 7.3 m/s and voy = 12.4 m/s. In unit-vector notation, what is the velocity of the cart when it reaches Number Units(a) Calculate the height (in m) of a cliff if it takes 2.30 s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of 8.07 m/s. (Enter a number.) m (b) How long (in s) would it take to reach the ground if it is thrown straight down with the same speed? (Enter a number.) s †
- During a test, a rocket travels upward at Va = 60 m/s and when it is Sa = 20 m from the ground its engine fails. Determine the maximum height Sb reached by the rocket and its speed just before it hits the ground. use 2 decimal places.The acceleration of a particle is a constant. At t=0 the velocity of the particle is (14.91 + 18.4ĵ) m/s. At t = 4.6 s the velocity is 11.4j m/s. (Use the following as necessary: t. Do not include units in your answers.) (a) What is the particle's acceleration (in m/s²)? = î+ 18.4 v(t) = (b) How do the position (in m) and velocity (in m/s) vary with time? Assume the particle is initially at the origin. r(t) = î+ X Î- i) m/s m/sA jet plane comes in for a landing with a speed of 120 m/s. The length of the runway is 500 m. From the instant the plane touches the runway, what is the magnitude of the acceleration needed to stop within the runway? Write your answer in terms of m/s2.
- The acceleration of an object (in m/s2) is given by the function a(t)=8sin(t)a(t)=8sin(t). The initial velocity of the object is v(0)=−10v(0)=-10 m/s. Round your answers to four decimal places.a) Find an equation v(t) for the object velocity.v(t)v(t) = −8cos(t)−2Correct b) Find the object's displacement (in meters) from time 0 to time 3.3.4187Incorrect metersc) Find the total distance traveled by the object from time 0 to time 3. metersAn article explains that the locomotion of different-sized animals can be compared when they have the same Froude number, defined as F = gl velocity, g is the acceleration due to gravity (9.81 m/sec2) and I is the animal's leg length. (a) Different animals change from a trot to a gallop at the same Froude number, roughly 2.56. Find the velocity at which this change occurs for an animal with a leg length of 1.12 m. (b) Ancient footprints of a dinosaur are roughly 1.4 m in diameter, corresponding to a leg length of roughly 5.6 m. By comparing the stride divided by the leg length with that of various modern creatures, it can be determined that the Froude number for this dinosaur is roughly 0.025. How fast was the dinosaur traveling? (a) The velocity at which this animal changes change from a trot to a gallop is (Round to the nearest tenth as needed.) where v is the animal's (...) m/sec.A student drops an object out the window of the top floor of a high-rise dormitory. (a) Neglecting air resistance, how fast is the object traveling when it strikes the ground at the end of 3.9 s? First used standard British units and then express the speed in mi/h for a familiar comparison. (ft/s and mi/h) (b) How far, in meters, does the object fall during the 3.9 s? Comment on how many floors the dormitory probably has. (Assume that there are 32 floors/100 m.)