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A physics question involving projectiles?

A tennis ball close to the ground is hit by a racquet with a velocity of 30m/s at an angle of 25 degrees to the horizontal. Find (a) The max height reached (b) The time of flight. Thanks

start by drawing a vector diagram, you need to split the velocity into both vertical and horizontal components, drawing the vector diagram makes this easily observed, all the vector diagram is is a right angle triangle with the initial velocity as hypotenuse and the two components of velocity are remaining sides,

Vv = Vi ( cos theta)

Vv = 30 sin 25 = 12.68 ms^-1

Vh = Vi (sin theta)

Vh = 30 cos 25 = 27.19 ms^-1

now, both time of flight and maximum height reached only require the vertical component of velocity to be calculated:

for a projectile that has a parabolic path and has a impact height the same as launch height we can use the following neat formula to calculate the time:

t = 2Vv/a ( where a =9.8 ms^-2 the acceleration at the surface of earth)

t = 2(12.68)/9.8 = 2.59 seconds

the projectile travels for 2.59 seconds in the air

the maximum height reached can be calculated using V^2 - U^2 = 2as

rearranging this we get v^2-u^2/2a = s

but we know that the final vertical velocity is zero because there is a change in direction, let a negative sign denote upwards direction of travel and positive sign denote downwards travel, by using this convention we can handle vectors mathematically.

as the projectile moves up then it has a negative acceleration. sub all this into the expression and we get:

s = (0)^2 - (12.68)^2/(-2x9.8) = -160.78/-19.6

s = 8.2 m

maximum height reached is 8.2 metres above ground.

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Strange strings which are IMPOSSIBLE to break..?

Recently I purchased another tennis racquet, the kfactor six, and my tennis stringer advised me to get these special strings.. This was about 2 months ago. Normally I break nylon, cow gut strings, and synthetic strings within about 2 weeks max. I've been playing with the strings I've gotten on and they've lost feel, the sweet spot is getting screwed up, and I'm getting pretty pissed off. The strings have what seems like to be something synthetic with metal inside? I've never seen this before. It can't be kevlar because kevlar is yellowish, hate those btw. The strings I got on are white/clear colored with silver/metal/idk what the heck it is but I REALLY want to know. Please and thanks before hand. Also, I'm requiring a detailed explanation for the ten points :]

i think this is polyester strings. if possible next time you have it strung pls ask the stringer what kind of strings he put into your racquet.

while poly strings are long-lasting, they feel really "dead" after a while. that's why some stringers recommend to use it in combination with synthetic/natural gut for adding some "feel". this combination is know as "Hybrid Stinging".

below i quoted some description from www.stringforum.net:

Polyester strings show a fairly simple structure: they consist of a single polyester fiber with a thin coating. This type of construction is termed "monofilament". They come in different gauges (1.10-1.35mm) which enables you to choose among different elasticity/durability levels. Polyester strings are little elastic and feel quite stiff compared to nylon or multifilament strings, but on the other hand they provide significantly better durability, allowing for thinner gauges. Pure polyester strings like the Polystar Classic or the Kirschbaum Super Smash have one main downside: They tend to lose their tension quite quickly, so control decreases and the string feels dead after a short time of play. Thus polyester strings are only recommendable for players with high string consumption. For these players, polyester strings offer a great price/performance ratio.

During the past few years, tremendous effort has been put into the advancement of monofilament strings and the elimination of their major weaknesses (tension loss and lack of elasticity). Luxilon has specialized in this string category. More and more polyester blends (co-polyester), mixed with a number of other materials like PEEK, carbon or metallic fibers, are being developed to modify the playing characteristics. Almost every manufacturer carries such strings in their program today.

Examples: Luxilon Big Banger Alu Power, Kirschbaum Touch Turbo, Signum Pro Poly-Plasma, Polyfibre Poly-Hightec, Head Ultra Tour.

hope this helps

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