2. A web page designer creates an animation in which a dot on a computer screen has a position of 7 = [4.0 cm + (2.5) t ] i+(5.0) e). (a) Find the magnitude and direction of the dot's average velocity between 1 = 0 and /= 2.0 s. (b) Find the magnitude and direction of the instantaneous velocity at / = 0, 1 1.0 s, and 1= 2.0 s. (c) Find the magnitude and direction of the instantaneous acceleration at 1 = 0, 1 = 1.0 s, and 1= 2.0 s.
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- 0, y 0) 44. A projectile is launched from the point (x QC with velocity (12.0î + 49.0 j) m/s, at t = 0. (a) Make a table listing the projectile's distance |r| from the ori- gin at the end of each second thereafter, for 0 s I S 10 s. Tabulating the x and y coordinates and the compo- nents of velocity v and v will also be useful. (b) Notice that the projectile's distance from its starting point increases with time, goes through a maximum, and starts to decrease. Prove that the distance is a maximum when the position vector is perpendicular to the veloc- ity. Suggestion: Argue that if v is not perpendicular to f, then r|must be increasing or decreasing. (c) Determine the magnitude of the maximum displacement. (d) Explain4. Let A = -4î+5ĵ, B = 7î - 9ĵ operations (a) D = A + 3B + С answers in vector notation. and C = −3î+8ĵ. Find mathematical and (b) Ẻ = 2Ả − B + 3C. Express yourAndrew has several tables filled with data describing moving objects. Which table has data thatdescribes an accelerating object?
- 7. A student goes for a jog at an average speed of 3.5 m/s. Starting from home, he first runs 1.8 km [E] and then runs 2.6 km [N 35° E]. Then he heads directly home. How long will the entire trip take?Part A) A projectile is launched with speed v0v0 and angle θθ. Derive an expression for the projectile's maximum height hh. Express your answer in terms of the variables v0v0, θθ, and appropriate constants. Part B) A baseball is hit with a speed of 34.0 m/sm/s . Calculate its height if it is hit at an angle of 30.0 ∘∘ . Express your answer with the appropriate units. Part C) A baseball is hit with a speed of 34.0 m/sm/s . Calculate its distance traveled if it is hit at an angle of 30.0 ∘∘ . Express your answer with the appropriate units. Part D A baseball is hit with a speed of 34.0 m/sm/s . Calculate its height if it is hit at an angle of 45.0 ∘∘ . Express your answer with the appropriate units. Part E) A baseball is hit with a speed of 34.0 m/sm/s . Calculate its distance traveled if it is hit at an angle of 45.0 ∘∘ . Express your answer with the appropriate units.A remote-controlled car is moving around in a level (horizontal) parking lot. The velocity of the car as a function of time is given by: 3 = [5.0m/s – (0.018m/s³)t²]î + [2.0m/s + (0.55m/s²)t]j where î and ĵ are unit vectors representing two perpendicular directions on the horizontal ground (think of them as the East and North directions, if that helps you). b). What are the magnitude and direction of the car's velocity at t = 8.0 s? c). What are the magnitude and direction of the car's acceleration at t = 8.0 s? (Don't be intimated by the velocity function! Look at the î and ĵ components, and work each component separately to begin with, before combining components together to get any resultant vectors, if needed.)
- A group of hikers sets out going 10.0km [N], then 15.0km [E], then 4.0km [S]. The entire trip takes 4.00h. Determine the magnitude hikers' velocity for the trip. 4.04 km/h [N 21.8° E] 5.25 km/h [N 21.8° E] 7.25 km/h [N 21.8° E] 21.0 km/h [N 21.8° E] 65.25 km/h [N 21.8° E]An object located at ?⃗0 = (1, 1) ? is displaced by Δ?⃗01 = −2?̂ − 5?̂ ? The object is then displaced by Δ?⃗12 = 3?̂ + 2?̂ ? a) Draw a picture b) What is the final position (?⃗2) of the object? c) How far did the object travel during each displacement? (?: 5.39 ?; 3.61 ?) d) What is the total distance travelled by the object? (?: 9 ?) e) How far did the object end up from where it initially started?(?: 3.16?)The velocity of a toy car moving along as straight path is shown in the figure. Match the numbers according to the graph. Assume the numbers in the choices are followed by proper units (not shown), i.e., distance in [m], speed or velocity in [m/s], and acceleration in [m/s^2].
- Problem 2: Kinematics and vectors. An object is moving on the xy plane with velocities given by: V₂ x = (10.0-0.500t)1 and v = (-5.00t+0.025²) j Determine the following quantities: a. The displacement of the object as a function of time. b. The average velocity of the object from for the time interval from 0 to 10 s.Bob has just finished climbing a sheer cliff above a level beach and wants to figure out how high he climbed. All he has to use is a baseball, a stopwatch, and a friend on the ground below with a long measuring tape. Bob is a pitcher and knows that the fastest he can throw the ball is about vo = 33.7 m/s. Bob starts the stopwatch as he throws the ball, with no way to measure the ball's initial trajectory, and watches carefully. The ball rises and then falls, and after t₁ = 0.710 s the ball is once again level with Bob. Bob cannot see well enough to time when the ball hits the ground. Bob's friend then measures that the ball hit the ground x = 123 m from the base of the cliff. How high above the beach was the ball when it was thrown? initial height: X 1₁ mThe velocity of a particle as a function of time is given by v(t)=(3t-t )i-4 j all in S.I. units. a) What are the dimensions of the "-1 " in the – ti term? What are the units of the "3 " in the 3t i term? b) Find the position vector of the particle, r(t), if r(0) = -5 i- 2j :) Find the time ti > 0 when the position in the i direction is a maximum. d) Find a 1 -> 3 the average acceleration vector in the time interval 1 to 3 seconds.