# 3.3 Projectile motion  (Page 8/16)

 Page 8 / 16

An archer shoots an arrow at a 75.0 m distant target; the bull’s-eye of the target is at same height as the release height of the arrow. (a) At what angle must the arrow be released to hit the bull’s-eye if its initial speed is 35.0 m/s? In this part of the problem, explicitly show how you follow the steps involved in solving projectile motion problems. (b) There is a large tree halfway between the archer and the target with an overhanging horizontal branch 3.50 m above the release height of the arrow. Will the arrow go over or under the branch?

(a) $\text{18}\text{.}\text{4º}$

(b) The arrow will go over the branch.

A rugby player passes the ball 7.00 m across the field, where it is caught at the same height as it left his hand. (a) At what angle was the ball thrown if its initial speed was 12.0 m/s, assuming that the smaller of the two possible angles was used? (b) What other angle gives the same range, and why would it not be used? (c) How long did this pass take?

Verify the ranges for the projectiles in [link] (a) for $\theta =\text{45º}$ and the given initial velocities.

$\begin{array}{}R=\frac{{{v}_{0}}^{}}{\text{sin}{2\theta }_{0}g}\\ \text{For}\phantom{\rule{0.25em}{0ex}}\theta =\text{45º},R=\frac{{{v}_{0}}^{}}{g}\end{array}$

$R=91.8\phantom{\rule{0.25em}{0ex}}\text{m}$ for ${v}_{0}=30\phantom{\rule{0.25em}{0ex}}\text{m/s}$ ; $R=163\phantom{\rule{0.25em}{0ex}}\text{m}$ for ${v}_{0}=40\phantom{\rule{0.25em}{0ex}}\text{m/s}$ ; $R=255\phantom{\rule{0.25em}{0ex}}\text{m}$ for ${v}_{0}=50\phantom{\rule{0.25em}{0ex}}\text{m/s}$ .

Verify the ranges shown for the projectiles in [link] (b) for an initial velocity of 50 m/s at the given initial angles.

The cannon on a battleship can fire a shell a maximum distance of 32.0 km. (a) Calculate the initial velocity of the shell. (b) What maximum height does it reach? (At its highest, the shell is above 60% of the atmosphere—but air resistance is not really negligible as assumed to make this problem easier.) (c) The ocean is not flat, because the Earth is curved. Assume that the radius of the Earth is $6\text{.}\text{37}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{km}$ . How many meters lower will its surface be 32.0 km from the ship along a horizontal line parallel to the surface at the ship? Does your answer imply that error introduced by the assumption of a flat Earth in projectile motion is significant here?

(a) 560 m/s

(b) $8\text{.}\text{00}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{m}$

(c) 80.0 m. This error is not significant because it is only 1% of the answer in part (b).

An arrow is shot from a height of 1.5 m toward a cliff of height $H$ . It is shot with a velocity of 30 m/s at an angle of $\text{60º}$ above the horizontal. It lands on the top edge of the cliff 4.0 s later. (a) What is the height of the cliff? (b) What is the maximum height reached by the arrow along its trajectory? (c) What is the arrow’s impact speed just before hitting the cliff?

In the standing broad jump, one squats and then pushes off with the legs to see how far one can jump. Suppose the extension of the legs from the crouch position is 0.600 m and the acceleration achieved from this position is 1.25 times the acceleration due to gravity, $g$ . How far can they jump? State your assumptions. (Increased range can be achieved by swinging the arms in the direction of the jump.)

1.50 m, assuming launch angle of $45º$

The world long jump record is 8.95 m (Mike Powell, USA, 1991). Treated as a projectile, what is the maximum range obtainable by a person if he has a take-off speed of 9.5 m/s? State your assumptions.

The phenomenon by which Protoplasm of a cell shrinks from the wall is
which vein connective from harm to Brian
which nevel succulate blood system from harm to hear
Burton
if an organism is cartilaginous is fully capable of a protecting the internal organs
what is different between cell and tissue
cell is the functional and structural unit of life while tissue is a group of cells aggregate to perform a similar or particular function
Tajudeen
cell is the basic unit of life while tissue is group of related cells that perform the same function Eg. the nerve tissue is made up of nerve cells
please what is meant by mutation
mutation is the change in DNA which results in the evolution
Shshank
what is binominal nomenclature?
the system of naming organisms depending on their xtics of origin
Vincent
The system of naming organisms using two-words Latin names
Agyeiwaa
what is the fate of reduced NAD in cell metabolism
what is plant cell
what is the importance of meoisis
it also aids in formation of pollen grain in anther and formation of ovules in ovary of flowering plant
Orawo
it also aids in formation of sperm or ova in animals
Orawo
explain the function of the skeleton
skeleton is mainly the infrastructure of the organisms
Shshank
what 's different between immunity and vaccination
vaccination simply refers to as drugs usually injected,most times in a liquid form given to a person or an animal,while immunity refers to a source of prevention usually in a liquid form that help in disease prevention
Grace
In children
Grace
Golgi apparatus helps in the formation of lysosomes
Diana
what is the difference between placenta and umbilical cord?
No difference
Onwane
what's golgi apparatus.
Grace
What is biology
is the study of living things
Kisa
biology is the study of living and non living things
Tinta
Biology is the study of living things
the study of living organisms
Furaha
Biology is the study of living organism or things
Rose
Biology is the study of both living and non living things
Funteh
distinguish between sex linked characters and sex limited characters
what is active transport
why is diffusion important
Jessy
dissolved substance move with in the cytoplasm by diffusion
Kisa
what role does mutation play in the process of evolution
Kisa
active transport refers to the movement of certain molecules or substances from lower to higher concentration with the help of energy or ATP
Shshank
mutation occurs due to change in DNA and DNA forms our body & if DNA changes then our body also acquire some changes & these changes gradually leads to the evolution of new species
Shshank
Got questions? Join the online conversation and get instant answers!