QUESTION 1 Supply all missing information with the correct numerical values. Do not include the units. Round off all answers to two decimal places. Do not forget the negative sign (-) if needed. A cannon ball is fired with an initial speed of 123 m/s at angle of 60 degrees from the horizontal. Express the initial velocity as a linear combination of its unit vector components. Vo = ( m/s) i +( m/s) At the maximum height, the speed of the cannon ball is v = m/s and the magnitude of its acceleration is a = m/s2 The time needed to reach maximum height is t= The maximum height reached by the cannon ball is H = m.
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- A trapper walks a 5.0-lan straight-line distance from her cabin to the lake, as shown in the following figure. Determine the east and north components of her displacement vector. How many more kilometers would she have to walk if she walked along the component displacements? What is her displacement vector?Ruth sets out to visit her friend Ward, who lives 60 mimi north and 100 mimi east of her. She starts by driving east, but after 20 mimi she comes to a detour that takes her 15 mimi south before going east again. She then drives east for 8 mimi and runs out of gas, so Ward flies there in his small plane to get her. 1. What is Ward's displacement vector? Give your answer in component form, using a coordinate system in which the y-axis points north. 2.What is the magnitude of Ward's displacement vector? 3. What is the direction of Ward's displacement vector?Dr. B takes her dog ada on a walk. they start out heading south for 0.75 miles. then they turn left 30 degrees and they continue to walk for another 11 mile. Finally they turn right 9o degrees and they walk 1.9 miles. The whole walk takes 45 minutes. What is the average speed of Dr.B and Ada on their walk? give your answer in m/s. What is the direction of the total displacement vector?
- Vector A has components Ax=−8.20 and Ay=11.7 . What is the magnitude A of this vector? ?=? Determine the angle θ in degrees between the calculated vector and the +x‑axis, measured counterclockwise from the +x-axis. ?=?From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 9.50 m/s and angle of 15.0° below the horizontal. It strikes the ground 6.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0. Assume SI units. Do not substitute numerical values; use variables only.) xi =____ yi =_____ (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity. vi, x =____ m/s vi, y =____ m/s c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: y0 and t. Assume SI units.) x =______ m y =_______ m (d) How far horizontally from the base of the building does the ball strike the ground? ___m (e) Find the height from which the…From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 8.30 m/s and angle of 25.0° below the horizontal. It strikes the ground 6.00 s later.(a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0. Assume SI units. Do not substitute numerical values; use variables only.)xi = yi = (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity.vi, x = m/svi, y = m/s (c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: y0 and t. Assume SI units.)x = my = m (d) How far horizontally from the base of the building does the ball strike the ground? m (e) Find the height from which the ball was thrown. m (f) How long does it take the ball…
- From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 7.50 m/s and angle of 18.0° below the horizontal. It strikes the ground 5.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0. Assume SI units. Do not substitute numerical values; use variables only.) xi = − yi = (c) Find the equations for the x- and y-components of the position as functions of time. (Use the following as necessary: y0 and t. Assume SI units.) x = y = (f) How long does it take the ball to reach a point 10.0 m below the level of launching?From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 8.80 m/s and angle of 16.0° below the horizontal. It strikes the ground 4.00 s later. (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (Use the following as necessary: y0. Assume SI units. Do not substitute numerical values; use variables only.) xi = yi =An athlete performing a long jump leaves the ground at a 31.8 ∘∘ angle and lands 7.65 mm away. What was the takeoff speed? Express your answer using three significant figures and include the appropriate units. If this speed were increased by just 4.0%, how much longer would the jump be? Express your answer using two significant figures and include the appropriate units.
- A cross-country skier skis 1.0 km north and then 2.0 km east. How far and in what direction is she from the starting point? What are the magnitude and direction of her resultant displacement? Show the Figure/FBD, given, formula and scale drawing usedFor the vectors shown in the figure below, answer the following question:The vector ?⃗ is given by ?⃗ = ? − 2?⃗ + 3? . Calculate the magnitude of ?⃗ as well as its direction withrespect to the positive x-axis. It is given that |? | = 3.0 units, |?⃗ | = 6.0 units, |? | = 5.0 units, = 60 and = 18.In 1780, in what is now referred to as "Brady's Leap," Captain Sam Brady of the U.S. Continental Army escaped certain death from his enemies by running over the edge of the cliff above Ohio's Cuyahoga River, which is confined at that spot to a gorge. He landed safely on the far side of the river. It was reported that he leapt 22 ft across while falling 20 ft. (Figure 1) A. Representing the horizontal distance jumped as L and the vertical drop as h , as shown in the figure, derive an expression for the minimum speed v he would need to make his leap if he ran straight off the cliff. Express your answer in terms of the given quantities and appropriate constants. B. Evaluate your expression for a 22 ft jump with a 20 ft drop to the other side. C. Is it reasonable that a person could make this leap? Use the fact that the world record for the 100 m dash is approximately 10 s to estimate the maximum speed such a runner would have. (Yes or no answer)