Name Date Period Free Fall: Acceleration Due to Gravity Chapter : Linear Motion INSTRUCTIONS: In this homework assignment, we will be looking at problems involving motion in the y-direction (up and down). In the world around us, gravity effects all objects motion when they are moving up or down. You have already seen the series of equations from chapter 5 which describe uniform acceleration. The letter a was used to represent acceleration in these equations. When dealing with falling objects (or objects moving up) the letter g can be replaced in each of the equations. Since we usually think of down being a negative direction, the acceleration due to gravity is equal to -g (a = -g). The magnitude of gravity is 9.8 m/s. We assign a value to g of -9.8 m/s because this describes a direction downward. Let s take another look at those equations from chapter 5 and replace a with g (acceleration due to gravity) v = v 0 + at substituting g v v + gt 1 d + at ( v v ) = solving for t 0 0 t = 1 gt = d 0 + v 0 t substituting g d = d 0 + v 0 t + When we can assume d 0 and v 0 equal zero (which they very often do), this equation becomes much simpler d = 1 gt solving for t t g = d g Definitions of each of the variables you see above: v = This is the final velocity (or velocity of impact) (units = m/s) v 0 = This is the initial velocity. Use a positive (+) value if you initially throw something up. Use a negative value (-) if you initially throw something down (units = m/s) If the initial velocity is zero (v 0 = 0), you can remove it from the equation. a = acceleration. When solving problems using gravity, substitute g for a (remember g is a constant at -9.8 m/s ) This is because gravity always acts downward. (units = m/s ) d = final distance. In the problems involving objects dropped, etc., d will represent the displacement in the y-direction. It is positive (+) if the final position is above where you threw it. It is negative (-) if the final position of the object is below where your threw it. (units = m) d 0 = initial distance. This is where the object started. This value is very often = 0 (d 0 = 0). In this case, you can remove it from the equation. (units = m) t = This the time the object is in motion. It is always positive. If you find it to be negative, then you did something wrong! (units = s) t 0 = This the initial time the object was put in motion. Yes I know, you do not see this in any of the equations above. That is because it was assumed in each that t 0 = 0, and was therefore eliminated from the equation. REMEMBER we arrived at each of the equations above from our two favorite equations of average velocity and average acceleration! 1
Motion Problems: Remember, when solving the kinematics motion problems, always follow these three steps: 1) Always start by writing down everything you know (the variables) and what they are asking you to find out (the unknown variable). Always show the units! ) The next step is to draw a visual representation of the problem (a picture) to help you keep track of what is happening and what you are looking for. You then need to draw a coordinate system (an x-y board) to determine (+) or (-) values for your variables. 3) Now choose which equation fits your problem and plug in the values and solve for your unknown. Problems: Questions 1: You drop a rock off the top of a building. It takes 4.5 s to hit the ground. How tall is the building? Step 1: List all variables you know and what you are asked to find. Step : Draw a diagram (coordinate system) and label. Keep in mind (+) and (-) values for g, v, etc. Step 3: Choose equation and plug in values to solve for unknown. Questions : You drop a rock off the top of a 100 m tall building. How long does it take to hit the ground? Questions 3: You drop a rock off the top of a building. It takes 3.4 s to hit the ground. What is the velocity at impact (final velocity)?
Questions 4: You throw a rock off the top of a building with an initial velocity of 5.0 m/s. It hits the ground going 5 m/s. How long did it take to impact on the ground? Questions 5: You throw a rock off the top of a building with an initial velocity of 7.0 m/s. It takes 5.5 s to hit the ground. What was velocity the rock hit the ground with (final velocity)? Questions 6: You throw a rock up into the air as hard as you can. It stays in the air a total of 6.0 s. What was the velocity of the rock when you threw it? Hint: If it stayed in the air for 6.0 s, how much of that was the way up, and how much time did it take to make it s way down..you re right...½ of the total time (6.0 s = 3.0 s) Hint number two: The velocity of the rock at the top of it s arc was what..you re right v = 0 Questions 7: You throw a rock off the top of a building with an initial velocity of 0 m/s. It takes 13 s to hit the ground. What was velocity the rock hit the ground with (final velocity)? 3
Questions 8: You throw a rock off the top of a building with an initial velocity of 10.0 m/s. It takes 1.0 s to hit the ground. How tall is the building? Questions 9: You throw a rock off the top of a building located on the Planet Mars with an initial velocity of 10.0 m/s. The force of gravity on Mars is ⅓ that of Earth. It takes 1.0 s to hit the ground. How tall is the building? Questions 10: You shot a gun straight up into the air with a velocity of 500 m/s. How long will it take before it hits the ground again? (Remember, we are disregarding the friction due to air) Refer to hints in question 6. Questions 11: You shoot a gun with a initial velocity of 500 m/s horizontally at the exact instant you drop a rock from exactly the same height (at 1.6 m off of the ground). Which one will hit the ground first. Show your math! 4
Create you own Motion Problem: You are to create two Motion problems involving gravity (in other words, motion in the up-and-down direction...you just completed 11 of them). Be as original as you can. You need to include the following: Create word problem. Create diagram (detailed) showing scenario (color would be nice). Label diagram and show all variables...be very neat! Show equation used and all math involved. The best questions will be used on a quiz! Motion Problem #1: 5
Motion Problem #: 6