You throw a stone vertically upward with an initial speed of 6.0 m/s from a third- story office window. If the window is 12 m above the ground, find (a) the time the stone is in flight and (b) the speed of the stone just before it hits the ground.
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- 81. •Astro The froghopper, a tiny insect, is a remarkable jumper. Suppose you raised a colony of the little critters on the Moon, where the acceleration due to gravity is only 1.62 m/s?. If on Earth a froghopper's maximum height is b and maximum horizontal range is R, what would its maximum height and range be on the Moon in terms of h and R? Assume a froghopper's takeoff speced is the same on the Moon and on Earth.• In heavy rush-hour traffic you drive in a straight line at 12 m>sfor 1.5 minutes, then you have to stop for 3.5 minutes, and finallyyou drive at 15 m>s for another 2.5 minutes. (a) Plot a positionversus-time graph for this motion. Your plot should extend from t = 0 to t = 7.5 minutes. (b) Use your plot from part (a) to calculate the average velocity between t = 0 and t = 7.5 minutes.2.9 .• A ball moves in a straight line (the x-axis). The graph in Fig. E2.9 shows this ball's velocity as a function of time. (a) What are the ball's average speed and average velocity during the first 3.0 s? (b) Suppose that the ball moved in such a way that the graph seg- ment after 2.0 s was – 3.0 m/s instead of +3.0 m/s. Find the ball's average speed and average velocity in this case. Figure E2.9 U, (m/s) 3.0 2.0 1.0 t (s) 3.0 1.0 2.0
- • 3. The velocity of a particle can be described by the function V(t) = 4 t² - 12t + 7 ( m/s) a) What is the instantaneous acceleration of the particle at t = 4? b) What is the average acceleration at time interval 3s & 5 s? c) The velocity when time is 3.5 s? d) The velocity when acceleration is zero. e) acceleration when the particles momentarily stopped or changes direction.• We learned the set of 1D-Kinematic equations that describe the Uni- formly Accelerated Motion to be structured as "position as a function of time", "velocity as a function of time", and acceleration = constant. It is possible with some maths to make an equation WITHOUT time that re- lates jsut the distance traveled, the uniform acceleration and the speed at the beginning at the end. This equation is: 2 ad = v – vố (1) where a is the said acceleration, d is the distance, and vo and vf are the initial and the final speed respectively. For an alternative notation follow the link: 1D-Kinematics The point of this homework is not to learn a new equation, but to practice equation properties in a new format. • State the units on the LHS and the RHS. Do they match up? • As you see the person (me) throwing the stone how much is the FINAL velocity? Restate the equation (1) with that information mind: • If you did everything right then you end up with your RHS NEGATIVE (!). That means that the…Problems • 1. A motorcycle stunt rider rides off the edge of a cliff. Just at the edge his velocity is horizontal with magnitude 5.0 m/s. Find the rider velocity and position after 1/4seconds.
- 44. ••Cody starts at a point 6 km to the east and 4 km to the south of a location that represents the origin of a coordinate system for a map. He ends up at a point 10 km to the west and 6 km to the north of the map origin. (a) Find his average velocity if the trip took him 4 h to complete. (b) Cody walks to his destination at a constant rate. His friend Marcus covers the distance with a combination of jogging, walking, running, and resting so that the total trip time is also 4 h. How do their aver- age velocities compare?• 4. An object's position is described by the following polynomial for O s to 10 s. S (t) = t3 - 15 t2 + 54 t where Sin meters, %3D t is in seconds. Determine : a) The object's Velocity Function3; b) The object's acceleration Function; c) The object's position at, t = 4 s; d) The object's velocity at, t = 4 s; %3D e) The object's acceleration at t = 4s; f) The time and velocity when object returns to its original position; g) The time and velocity when acceleration is zero. h) Is the object's speed is increasing, decreasing, either if time is 4 s ? - NOTES E UELDIMDDOVE OFFICE•A soccer ball is kicked with an initial speed of 8.25 m>s. After0.750 s it is at its highest point. What was its initial direction ofmotion?
- • Part A Gulls are often observed dropping clams and other shellfish from a height to the rocks below, as a means of opening the shells. If a seagull drops a shell from rest at a height of 13 m, how fast is the shell moving when it hits the rocks? Express your answer using two significant figures. ? m/s Submit Request Answer Provide Feedback Next >2.6 .• A Honda Civic travels in a straight line along a road. Its distance x from a stop sign is given as a function of time t by the equation x(t) = at? – Bt, where a = 0.0500 m/s. Calculate the average velocity of the car for each time interval: (a) t = 0 to t = 2.00 s; (b) t = 0 to t = 4.00 s; (c) t = 2.00 s to t = 4.00 s. 1.50 m/s? and ß %3DA celebrated Mark Twain story has motivated contestants in the Calaveras County Jumping Frog Jubilee, where frog jumps as long as 2.2 m have been recorded. If a frog jumps 2.2 m and the launch angle is 45, find (a) the frogs launch speed and (b) the time the frog spends in the air. Ignore air resistance.